The problem with this is most things from outside (like insects or maybe a mouse) likely have been exposed to many things that would be harmful to the captive animal. Insects, e.g. may be contaminated with harmful bacteria, fungus, or toxins like pesticides. All these may kill or poison your beloved animal.
However, if it does not harm the animal, it may still infect the enclosure. For example, if a small insect is carrying some bacteria or fungus, it may spread to the substrate or decor within the enclosure, causing multiple problems, and then potentially even killing the animal because of exposure. Even another situation that happens is perhaps the feeder animal is pregnant, e.g. a cricket and before it is consumed, it may give birth, causing an infestation, bringing significant problems for your animal and yourself down the road.
Therefore, it is strongly advised not to feed your animals anything from outside, but instead, using feeder animals from a reputable breeder. It is a safer and better option.
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The power of imagination makes us infinite. – John Muir