So once you use this ring to steal an equipment from someone wouldn't you un-equip the ring?

Larfleeze can be equipped with multiple objects that’s part of his trait.

@shawn11189 Sure but anyone can have the ring equipped.

When you unequip someone of their equipment you do not auto equip it unless the effect specifically says you can, they just don't have it on them at that point.

Without an errata, or special character rules, the updated (revised for 2022) parts of the Comprehensive Rules (25.2d) indicate that the Orange Ring would be unequipped via the Plasticity/Close Attack usage of the Orange Ring, if you choose to equip another object. For now, it's Larfleeze (and his traited Plasticity, and his traited NOT YOURS!) that can (optionally) accumulate multiple equipment during the game. I don't see that there is a choice to force another character to unequip and NOT also equip that equipment. This is the only part that I think could use a clarification.