Offer a specific task you can take over instead of another decision someone tired must make.

Exhaustion makes choosing harder than doing. Someone deep in a difficult period has a head full of small decisions already, and asking them what would help adds one more to the pile, however kindly it is meant. Naming the thing you will do removes a decision instead of creating one.

Pick something concrete and say you are doing it unless they would rather you did not. Collecting the prescription, taking the dog on Wednesdays, sending a meal on Sunday. Keep it small enough that it is easy to accept and regular enough that they do not have to ask again.