I would imagine that people willing to go to Mars permanently would be among the more scientifically minded and they wouldn't be stopped by concerns about what happens with dead matter left after them. The very last one could be cremated and buried by automatons. We have bodies laying frozen on Mount Everest today.

But I expect that either civilization would be able to resupply them with people or even connect them back eventually, or alternatively (if we do decline) too much stuff would be happening on Earth for people to really notice the fate of Martians.