There was a good comment on r/oil by someone who worked on the engineering for the SPR. Unfortunately it's fallen off the front page and I can't find it now, but:

> Also, the more water we pump in, the more salt leeches into the water and the more the bottom of the chamber deforms, creating shear forces in the upp walls that lower its overall structural integrity.

It turns out that it's trivially easy to prevent the water from leeching out the salt. They presaturate the water with salt, so that it already contains the maximum amount of salt that can be dissolved for a given temperature. When they pump the brine out, it goes into aboveground brine pools that can easily be seen on satellite imagery. The salinity of this brine can easily be controlled: if you want to expand the cavern, you mix it with freshwater so the brine dissolves more of the edges, if you don't you pump it back in as brine.

Edit: Here, found some satellite imagery of one of the SPR sites:

https://maps.app.goo.gl/B8XJ9TVhQfcdErky5

You can clearly see the brine pond, which is as big as the aboveground portion of the SPR itself.