The shower stall has not been installed correctly. The acrylic resin ones do bend when someone steps inside, so the proper way to install them is to put some support below the pan, in the center, to make sure they don't move.
Usually the shower pan comes with feet. If it does not, for example you would lay a few bricks on their side, pour some plaster on top, then set the shower pan on top. Or just plaster if you need less than an inch.
If it is reasonably easy to remove the shower pan, you can remove it and install it properly, with support. That will fix your silicone caulk tearing problem. You can also check if whatever the shower pan lies on is strong enough to support it, or if it is rotten. The problem could come from the shower pan being installed on a support that isn't strong enough and bends, like thin or rotten wood. That's less easy to fix though!
A more "quick and dirty" solution is to make a hole in the side of the pan near the floor and inject a can of expanding foam below it, so the pan is supported from below. If you do that, put some weight in the pan, otherwise the expanding foam will lift it.
Expanding foam isn't as strong as a brick, and it won't fix the floor if the problem is a rotten/bending floor, so this is a "meh" solution, but it is reasonably cheap and much easier to do.
A more temporary solution would be to do a caulking job that doesn't tear. It's not guaranteed to work, but it's better than nothing.
Basically, silicone caulk can stretch by a certain amount before tearing. A larger joint can stretch more before it tears. So the solution is to make a larger joint. First remove the old caulk and grout. If you leave the old rigid grout in, your silicone joint will be thinner, and more prone to tearing. Then apply new caulk and smooth it with a rubber corner smoother like this:
If you don't want it to tear off from the tile, it should be large enough to cover it for at least 2-3mm. Also put some weight in the pan while the silicone cures. You can use a large barrel filled with water, sand bags, whatever.
Since it's a bathroom, you should only use mold-proof silicone. Other types of caulk (urethane, acrylic, etc) are not designed to withstand household cleaning products like bleach.
In any case you have to fix this. If you don't, water will keep leaking out. If the building structure is wood, it will rot. Even if it is a water resistant material like concrete, water seeping out will cause stains and mold on the ceiling in the floor below. Once the building materials are waterlogged, it takes a very long time to dry.
So if you don't fix it today, it would be a good idea to put some tape over the crack right now as a temporary seal.
