There should be a pipe coming from the box with the coils in it that is supposed to drip/drain. It should be over a drain in the floor, or somehow flowing into your pipes.
The water it drains is just the condensate that builds up as the warm air blows over cold coils. When people talk about "freezing coils" I'm a little iffy on how this causes water leaking. If air-flow over the coils is inadequate, then ice could build up on the coils, completely blocking air flow and preventing your house from cooling. That ice will melt, but the drain-pipe (if clear) should handle it. There is no other water inside your house related to air conditioning that I know of.
If the condensate drain pipe clogs, the water that should drip from that pipe into the floor rain is going to flow somewhere else. On my system, that somewhere else was a pipe not really over the drain, leading to wet carpet. I cleared the draining pipe and that was all it took. For me, the entire condensate management system was just gravity. Water dripped from the coils to a pan, then from the pan to the PVC pipe then to the floor drain. No pumps or anything.