What should a cell phone repair shop owner do after hundreds of uncollected phones have accumulated, some of which have been repaired and some have not, and they have been with him for years?

These mobile phones are a trust with you until their owners come. You have the right to demand from them the expense of their safekeeping, which is in addition to the repair cost, when they retrieve them. As for the mobile phones whose owners you have despaired of ever coming, dispose of them in charitable and benevolent ways.