It happens to all of us. One Lego block is missing, or that single puzzle piece isn't with the rest of the jigsaw. You know it will always be in the last place you look ;-)
Here are some tips to reduce the risk of toy pieces getting lost.
If you've borrowed a fabulous toy with lots of itty-bitty pieces, think about whether your child really needs to play with all of them. For example, the farm set has four chickens, three cows and two pigs - but the chickens are smaller and more likely to get lost. Maybe put two chickens and one of the cows back in the bag for safekeeping - there's still a lot of action happening on the farm!
If you borrow a toy set which already has some similar pieces to ones you own (eg Lego), perhaps substitute your own and keep the toy library pieces in the bag - no risk of losing them then!
If a borrowed toy comes with smaller pieces which are more likely to be lost, why not keep them safe in a box so you can bring them out when you're playing with your child and then put them back. Less clutter = less chance of pieces disappearing.
Start collecting all the toy pieces a day or two before you plan to return them, giving yourself lots of time to check under the couch and in all the other hidey places before you come back.