Yes if someone dies, they can be replaced by extending duty shifts, if VOY was on a 4 shift rotation, with diminishing crew numbers it might have to go a 3 shift rotation. And the length of each shift might increase from 6 to 8 to 10. Yes there might come a time when extending shifts couldn't be done. Which might mean less important things i.e. repairing every interior corridor so it looks like it had just left Utopia might not being completed.
In the workplace if someone leaves, you can't always replace them but the same amount of work still has to be done. So the rest have to pick that up.