What does Jesus mean that those that can be trusted on small matters can be trusted in large matter?

Where you seem to be missing the mark is in trying to compare the situation that the parable describes to modern day, while it is the message that Jesus was teaching that should be studied as how does this apply to me today.

The message Jesus wanted them and us today was not that Trust is connected to whether we are faithful with the small things and therefore we are trustworthy with larger things.

Jesus was teaching those around him two very important things;

Luke 16:1 and 2 KJV And he said also unto his disciples, There was a certain rich man, which had a steward; and the same was accused unto him that he had wasted his goods. And he called him, and said unto him, How is it that I hear this of thee? give an account of thy stewardship; for thou mayest be no longer steward.

Jesus wanted them and us to understand that just as the unfaithful servant we stand
the risk of heading down a path of dishonesty and once on that we can either repent
and keep the blessings of our masters, or continue down that path to judgment and our
own destruction.

secondly Jesus was saying to them that to continue down that road to destruction is
to secure a the same fate as all other unfaithful people. (the debtors owed the owner
and not the servant, and they were robbing him just as the servant was.)

Luke 16:3 through 9 KJV Then the steward said within himself, What shall I do? for my lord taketh away from me the stewardship: I cannot dig; to beg I am ashamed. I am resolved what to do, that, when I am put out of the stewardship, they may receive me into their houses. So he called every one of his lord's debtors unto him, and said unto the first, How much owest thou unto my lord? And he said, An hundred measures of oil. And he said unto him, Take thy bill, and sit down quickly, and write fifty. Then said he to another, And how much owest thou? And he said, An hundred measures of wheat. And he said unto him, Take thy bill, and write fourscore. And the lord commended the unjust steward, because he had done wisely: for the children of this world are in their generation wiser than the children of light. And I say unto you, Make to yourselves friends of the mammon of unrighteousness; that, when ye fail, they may receive you into everlasting habitations.

Lastly Jesus is telling them God's outlook toward those actions in the trust analogy.

Luke 16:10 through 13 He that is faithful in that which is least is faithful also in much: and he that is unjust in the least is unjust also in much. If therefore ye have not been faithful in the unrighteous mammon, who will commit to your trust the true riches? And if ye have not been faithful in that which is another man's, who shall give you that which is your own? No servant can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon.

If You do not have the basic principles of honesty, integrity, and etc. so that you
do not exercise proper care of what he gives you here on earth, why should God give
you the riches of Heaven since indications are that they would have no more value to
you than what he has already entrusted to you.

Hope this helps.

Well first its a simple ideal not to be overly drawn upon because not every individual is the same but in a general sense if you really think about it, the statement is true. If I can trust my daughter to be responsible with something I can detetmine wether or not she could be responsible in another situation, if a man does great governing one district than I may find him fit to govern three districts or four

What I took from this verse is that, faithfulness is a virtue God wants us to possess it’s a positive thing. If you have a little, it’s like a seed and it grows with continued devotion. There is potential to have great faith. Lying is sin, but it’s also like a seed, it grows. Lies start out small and they grow larger in time.

Madoff proved himself to be a brilliant con man. People who invested with Madoff assumed he was a trustworthy person because he at one point made them a small amount of money/ROI. So, once he had their trust, he was able to convince them to invest large amounts of their money which unfortunately were funneled into his devious con man schemes.

You have made the assumption that if a stock broker makes you a little bit of money, then that automatically makes them trustworthy enough to give them larger amounts of money to invest with.

I believe Jesus is referring to a person's character when He says that a person who can be trusted in small matters can also be trusted with larger matters. When it comes to stock trading, its yours and everyone else's responsibility to verify that the stock broker is a person of good character before you give him/her a lot of money.

You should therefore always spend some time investigating a person's character to determine whether that person is truly trustworthy, instead of just relying solely on how much money they reportedly have made for investors in the past.

With parables you have to remember that they are directed at a specific audience, and make a specific point. Trying to extrapolate to draw conclusions outside the purpose of the parable would lead to a wrong conclusion. Parables are also used to illustrate general principles, not to lay down hard and fast rules.

In the Parable of the Talents, the point is about the behaviour of the servants. Jesus makes that pretty clear from context. The conclusions the hearer should draw are about parallels to the servants, not to the master. So (to simplify a little) the lesson from this parable is "work hard with what you are given to generate 'profit' for your master". You could also reasonably infer the lesson: "show yourself trustworthy in small things so that you will be trusted with larger things". (That's different from the lesson you are talking about.)

To derive a lesson that "anyone who is trustworthy with small things is also always trustworthy with large ones" would be outside the scope of the parable. It's focussing on the wrong part of the parable. The character in the story doesn't say it is a general rule, but only as something specific to another character: "Because you have shown yourself trustworthy in small things..." We shouldn't infer that it is applicable in all cases.