Does "all Israel shall be saved" mean that all Jews, even those who die in their sins, will be saved?

This is a nondenominational view as it is taken from the Bible mainly, but enhanced by the commentary of David Guzik.

In this passage Paul is referring to the book of Isaiah:

Isaiah 4:2 through 4 In that day shall the branch of the LORD be beautiful and glorious, and the fruit of the earth shall be excellent and comely for them that are escaped of Israel. And it shall come to pass, that he that is left in Zion, and he that remaineth in Jerusalem, shall be called holy, even every one that is written among the living in Jerusalem: When the Lord shall have washed away the filth of the daughters of Zion, and shall have purged the blood of Jerusalem from the midst thereof by the spirit of judgment, and by the spirit of burning.

And he was connecting this to Jesus, The following is an excerpt from The commentary of the whole Bible by David Guzik:

God's plan for Israel includes their eventual restoration.

(verses 25-27) The promise that all Israel will be saved. For I do not desire, brethren, that you should be ignorant of this mystery, lest you should be wise in your own opinion, that blindness in part has happened to Israel until the fullness of the Gentiles has come in. And so all Israel will be saved, as it is written: "The Deliverer will come out of Zion, and He will turn away ungodliness from Jacob; for this is My covenant with them, when I take away their sins."

a. Paul's warning to us that we should not be wise in your own opinion should remind us to take what he says here soberly. Christians must not be ignorant of this mystery.

b. Blindness in part has happened to Israel: Paul summarizes his point from Rom. 11:11-24 is summarized. God's purpose in allowing hardening in part to come upon Israel is so that the fullness of the Gentiles can come in.

i. In part has the idea of "temporary"; Israel's hardness is temporary. "One day the Jews will realize their blindness and folly. They'll accept Jesus Christ, and the glorious national restoration of these people will bring in the Kingdom Age." (Smith)

c. However, when that fullness of the Gentiles has come in, God will once again turn the attention of His plan of the ages specifically on Israel again, so that all Israel will be saved. God's plan of the ages does not set its attention on everyone equally through all ages.

d. All Israel will be saved: This all Israel is not spiritual Israel. It isn't "spiritual Israel" in Rom. 11:25, because that Israel is spiritually blind. Therefore, we shouldn't regard it as spiritual Israel in Rom. 11:26.

i. There is a distinction between national or ethnic Israel and spiritual Israel. Paul makes this clear in Gal. 3:7 and other passages. Nevertheless, God still has a purpose and a plan for ethnic Israel, and will bring salvation to them.

ii. Another proof that this is not spiritual Israel is because Paul says this is a mystery - and it is no mystery that spiritual Israel will be saved.

iii. Harrison on all Israel: "It was the view of Calvin, for example, that the entire company of the redeemed, both Jew and Gentile, is intended. But Israel has not been used of Gentiles in these chapters, and it is doubtful that such is the case in any of Paul's writings."

iv. "It is impossible to entertain an exegesis which understands Israel here in a different sense from Israel in verse 25." (Bruce)

e. Will be saved: This states clearly for us that God is not finished with Israel as a nation or a distinct ethnic group. Though God has turned the focus of His saving mercies away from Israel on to the Gentiles, He will turn it back again.

i. This simple passage refutes those who insist that God is forever done with Israel as Israel, and that the Church is the New Israel and inherits every promise ever made to national and ethnic Israel of the Old Testament.

ii. We are reminded of the enduring character of the promises made to national and ethnic Israel (Gen. 13:15 and 17:7-8). God is not "finished" with Israel, and Israel is not "spiritualized" as the church.

iii. While we do see and rejoice in a continuity of God's work throughout all His people through all generations, we still see a distinction between Israel and the Church - a distinction that Paul is sensitive to here.

f. All Israel will be saved: This does not mean there will be a time when every last person of Jewish descent will be saved. Instead, this is a time when Israel as a whole will be a saved people, and when the nation as a whole (especially its leadership) embraces Jesus Christ as Messiah.

i. Even as the apostasy of Israel did not extend to every last Jew, so the salvation of Israel will not extend to every last Jew; Paul is speak of the "mass" of Jews when he says all Israel. "All Israel is a recurring expression in Jewish literature, where it need not mean 'every Jew without a single exception', but 'Israel as a whole.' " (Bruce)

ii. And, when all Israel will be saved, they will be saved through embracing Jesus Christ as Messiah - as unlikely as this seems. They are not saved with some peculiar "Jewish" salvation.

iii. The Bible indicates this is a necessary condition for the return of Jesus Christ (Mat. 23:39, Zec. 12:10-11). Jesus will not return again until God turns the focus of His saving mercies on Israel again, and Israel responds to God through Jesus Christ.

g. The Deliverer will come out of Zion: The quotations from Isaiah show that God still has a redeeming work to accomplish with Israel, and that it will not be left undone.

Paul is asserting that one day Israel as a nation will accept that Jesus was the promised messiah, and will become a Christian Nation. We do not know when this will happen, but some other writings by Paul seem to indicate that this will be very close to the second coming, and may even be during the first part of the tribulation, when the Temple is rebuilt.

Whatever the circumstance it is clear that when this happens the millennial reign of Christ is close at hand.

Hope this helps.

I hope these numbers 673 and 674 in the Catechism of the Catholic Church shed some light

The glorious advent of Christ, the hope of Israel

673 Since the Ascension Christ's coming in glory has been imminent,[cf. Rev 22:20]. even though "it is not for you to know times or seasons which the Father has fixed by his own authority."[cf. (Acts 1:7; Cf. Mk 13:32.)]. This eschatological coming could be accomplished at any moment, even if both it and the final trial that will precede it are "delayed".[cf. Mt 24:44; 1 Thess 5:2; 2 Thess 2:3-12].

674 The glorious Messiah's coming is suspended at every moment of history until his recognition by "all Israel", for "a hardening has come upon part of Israel" in their "unbelief" toward Jesus.[cf. (Rom 11:20-26; cf. Mt 23:39.)]. St. Peter says to the Jews of Jerusalem after Pentecost: "Repent therefore, and turn again, that your sins may be blotted out, that times of refreshing may come from the presence of the Lord, and that he may send the Christ appointed for you, Jesus, whom heaven must receive until the time for establishing all that God spoke by the mouth of his holy prophets from of old."[cf.Acts 3:19-21.]. St. Paul echoes him: "For if their rejection means the reconciliation of the world, what will their acceptance mean but life from the dead?"[cf.Rom 11:15.]. The "full inclusion" of the Jews in the Messiah's salvation, in the wake of "the full number of the Gentiles",[cf. (Rom 11:12, 25; cf. Lk 21:24.)]. will enable the People of God to achieve "the measure of the stature of the fullness of Christ", in which "God may be all in all"[cf. (Eph 4:13; 1 Cor 15:28.)].

The understanding here is "full inclusion of/full number of" vs. "all [of]".

Suppose the LORD has invited g number of gentiles and j number of Jews before he comes. Some reject his call. g reaches fullness first then j - recalling he went to call g after most of the first j called rejected him. The LORD comes when the number g + j is reached.

"My church believes that if you die in your [mortal] sins, there is no further hope for you. Jewish or not." - This is the Catholic Teaching as well.

All of Romans 9-11 should be read together. Paul was responding to the accusation that God's promises to Israel had failed, and his response is basically: "you misunderstand what God means by 'Israel'; it is only the remnant of Israel's natural descendants that count as 'Israel', so actually, all Israel will be saved and God's promises have not failed".