So I decided to summarise the info on this interesting glitch, which doesn't seem to be useful for speedruns, however, still is pretty amusing and can theoretically help in extreme situations.

First of all, videos. With cheats. Without cheats.

What is the trick? It depends on two things. First of all, special busting animation should occur. Besides usual animation, during which cop needs to open door first, there is another which occurs while player is entering a car. Here are two gifs of busts showing both animations. Regular:

Special: The second one can lead to invincibility glitch. The thing is that player is set to be busted even before he gets in the car. To avoid unexpected outcomes it was programmed that player can't die until he fully enters the car. However, there is a way to cancel entering animation, by blowing up the car during it. Player will not die and since he is set to become invincible until he gets in the car, he remains invincible.

Car can be blown up at least in two ways. First and easy one is to type blowing up cheat during animation. Second one is to set car on fire beforehand and then get in.

Getting the necessary animation is more tricky. There is a consistent way to get it: if player punches cop and immediately enters the car (while cop is still recovering), this animation will occur. It is a bit more tricky without a cheat because cop should be near a car so that player can quickly enter it, and it takes time to damage a car. It also seems more consistent if cop has already pulled out a pistol.

Damage that should be dealt to the car is at least 750 but no more than 1000 (8 or 9 shotgun pellets or 15-19 M16 bullets unless car is damaged too much) for it to start burning and not to explode.

Also since player is set to be busted, he can't enter any car until whatever remains of busting cop still exist, otherwise he will be busted.

Now about invincibility itself. While player is on foot nothing at all can kill him: not bullets, fire and explosions, not cars running him over, not water and not even crusher, which normally sets health to zero if player gets inside it. While player is in car he still doesn't take damage from water. But if a car gets blown up with a player inside, he dies. Also player still can be busted.

The unfortunate part about it is that invulnerability is removed by opcodes 01B4 with parameter 1 (remove frozen state) and 02EA (end cutscene) if there actually was cutscene. So this basically means that any mission removes invincibility. However it works with rampages and regular gameplay.

This glitch also works in Vice City and was originally discovered by KAS.