He'd let go already, and it was a weakness to grasp for things he couldn't ever touch again (and if his fingers were warm where Yata had touched him, well, then that was only the blood on his hands marking deep).
It wasn't something Fushimi had ever really thought about, taking care of someone.
In the immediate aftermath of the Ashinaka High Incident, Fushimi does paperwork, Yata mourns, and the world is not so small. Sarumi, post-series.