If I use a readied action to disarm an enemy if they attack and succeed, rendering them incapable of continuing their attack, do they get their standard/full action back to do something else, or do they lose that action entirely?
They get the rest of their full attack. If they have another weapon on hand to use or draw as a free action they can use it instead as normal (a character with quick draw and iterative attacks, could stab you with a sword, drop it, draw a dagger as a free action and stab you with it as its next attack). If they have the ability to do so they could convert the remaining attacks into combat maneuvers, such as attempting to disarm you in return. Finally, if they are desperate they may use the remaining attacks to attempt unarmed strikes. These attacks or combat maneuvers may or may not provoke depending on what abilities they have.
If after being disarmed the creature does not want to make any additional attacks/maneuvers with what they have left, they do not have to.
Yeah, many enemies will have backup weapons they might be able to draw for free depending on their feats, they may have natural weapons, they may just punch you.
Also, in PF1 there isn't much reason for people who aren't spell casters to not use a locked gauntlet, and as a GM it's something I regularly add to NPCs.
And almost everyone should invest in armor spikes or a cestus to always have a back up weapon. It may not be very good, but it will at least let you keep making attacks.
You'd also want to do it after their second attack, technically they can choose not to make a full attack between making their first and second attack, if you disarm them after the first they can just choose to only make a standard action attack and do something else with their move action.
Deciding between an Attack or a Full Attack
After your first attack, you can decide to take a move action instead of making your remaining attacks, depending on how the first attack turns out and assuming you have not already taken a move action this round. If you’ve already taken a 5-foot step, you can’t use your move action to move any distance, but you could still use a different kind of move action.