Brake caliper Bolt rubber sleeve

Nope. There's a rib on each end to hold the sleeve in place. Replacements come in the hardware kit that is available for all cars and trucks. The more expensive kits only cost around ten bucks at most auto parts stores.

One of the biggest problems is caused by dirt or rust built up on the mounting bolts. That won't be a problem with your new bolts, but if the chrome plating had lifted on the old ones, that would have torn up the inside of the sleeve. To prevent that, part of a standard brake job is to coat the bolts, (any a few other critical places), with special high-temperature brake grease. Without that, usually the only problem at first is the caliper is hesitant to release fully, and accelerated outer pad wear will be seen.

You also must check the sleeve's bore to be sure no rust has built up in there. One potential clue is the bolts won't slide in easily. That rust, if not cleaned out, and torn sleeves, will cause the caliper to not sit squarely to the rotor. The only way a caliper can turn a little is if the piston retracts too much. That eliminates the self-adjusting feature of a disc brake, and will result in the brake pedal traveling too far to the floor. What you thought was an adhesive holding the sleeve in was actually that built-up rust.

You can use that brake grease on the outside of the sleeves too. That will make them slide in easier, and can reduce the formation of that rust. Brake grease will not smoke when it gets hot, and it won't migrate to the friction surfaces like petroleum-based grease would.