Missing funding deadline for serious reasons: what to do?
Of your options, I can think of no reasons not to try option 2. The worst thing that happens is that they say no. Option 1 is probably not going to work unless the deadline was missed by less than a day.

What your friend should do/should have done is emailed the committee as soon as they reasonably could regarding their situation. I would imagine that informing the committee of their situation and asking for a small extension has the best chance of going over well. The longer they wait to turn in their application or contact the committee, the less likely they are to be accepted.