Upvote:1
Assuming you leave Germany directly, leaving 1 day after the residence permit has expired is no problem.
Should your citizenship require a visa for other Schengen Countries, the residence permit can only be used as a visa replacement while it is valid.
Accourding to the Administrative regulation (quoted below), a period of 1 month is considered to be 'without delay'.
Verwaltungsvorschrift: 50.2.3
Eine Ausreisefrist von einem Monat nach Beendigung des rechtmΓ€Γigen Aufenthalts ist im Regelfall ausreichend.An exit period of one month after the end of the legal stay is usually sufficient.
Sources:
Such foreigners must leave the federal territory without delay or,...