I think it would vary from individual to individual, group to group. I like the idea (from Bolo'Bolo, which I've still never actually read) of taku (a box 50x50x100cm) which holds a person's posessions. If it fits, it is theirs, if it doesn't it isn't, Would probably make dividing everything up a lot easier once they were dead.
I do think there is something to be said for items of sentimental value going to people that care about those sentimental items, but then again, depending on what someone feels sentimental about, that could easily lead to the accumulation of capital, and that is a big old shitshow (as evidenced by our current state of shitshowiness).
Honestly, I think it would be very dependent on the particular group of anarchyists, and the material realities of the moment. There is no way to be prescriptive about this.