Investors don't vest and (to a first approximation) can't be fired. (They can constructively "quit", by refusing to answer your emails, but they keep all their equity and you keep all their money.)
The question of whether they "legally receive the shares right away" can be a bit more nuanced, particularly in e.g. a transaction for a SAFE or convertible note.
E.g. if they put in 1M for 25%, do they legally receive the 25% of shares right away?
What's typical here? In terms of investor vesting relative to the founders.