All pets like toys, but the rescue pets really need distractions and fun. They also come with more issues so need patience in even learning how to play. Most toys are destructible and won’t last long, so while trying to teach them to be less destructive consider making your own toys.
This is this disclaimer as I have researched many ideas and they all could have some problems for some pets. Always think about the pet’s safety, but no need to get crazy about these things unless you leave the pet playing with an untested toy alone. Playtime, till problems are known, should be with humans in attendance. You can then adjust the toy made and change it for better size or better durability, and address possible chewing or swallowing problems. This should probably even be done with toys bought at pet stores. After reading some comments on websites where suggestions were made, the thought occurs that hopefully they worry about their children as much. T
oys should obviously not be so small for the dog size that there is a danger of swallowing something not meant for consumption. The size of a toy can be a characteristic that determines if they like it or not. The wrong size may prevent them from playing with it.
If you can tie knots, a toy can be made. Braid and tie toys for tugging. Wrap and tie toys for different shapes that the pet will like. These can be thrown or just carried around by the pet. Anything that can be twisted into shapes and has some durability will make a good toy. Use old denim, old shirts, towels, rugs, even rope from which to make pet toys. Indoor Frisbees can be made out of braided cloth. You can braid cloth and use it in many shapes for pulling and tugging. You can make your own stuffed toys and for cats fill them with loose catnip.Don't forget boxes and yarn as simple cat toys. There are many ideas with socks tied with something inside such as an empty plastic water of pop bottle. Put something inside like that and tie the sock securely. There are pets that just loved the plain empty plastic bottle and enjoyed them for hours even without the sock. They will like the softness as well as the crunch of the bottle.
An empty milk jug can be great just as it is, best to remove the lid though. In the past destructive puppies played with bag balls, made up of stuffed and tied plastic bags. It should be very tightly tied so it cannot come apart. As with all toys watch their play carefully to be sure they cannot get it apart and swallow any plastic.
A tennis ball is still one of the most ideal of toys. Besides throwing it, you can make a small slit and stuff dog treats inside. It will then have a rattle and alluring smell.
If the truth be known , first choice in play things is another pet or a human.