Hello
your wife's plant is "echinopsis subdenudata" (without thorns) or "pseudo echinopsis" ("false", in reality, in some they can appear very small and white like my twisted depicted above)
The whole genus of echinopsis produce very beautiful flowers, even 20 cm long (7.87) and usually bloom at night hence the name of "beautiful at night"
Usually, when they are soggy especially at the base is a sign of rot due most often to too much stagnant moisture, lethal to succulents and the plant is doomed.
If so, the only remedy is to cut with a very sharp blade all the rotten part, let it dry for a few days (even a month if necessary) and then repot it in a bowl with three parts of common field land (very lean then) and only a part of universal land for generic plants, hoping that over time it will produce new roots.
The achinopsis produce them easily, a little less the "subdenudata" but still possible
Be careful though, your wife's plant does not seem to have rot from what I see in the picture, (moreover it would not have produced any flower if it had rot) it seems rather in a resting stasis and therefore the roots no longer absorb water for a certain period
You should moderate the watering at this time and keep an eye on it for a period of time and if you insist this condition it is likely that not the plant but the roots have rotted, (it has already happened with one of mine of this spacie, since it has more delicate roots than other echinopsis) so it would be appropriate to remove the plant from the pot and check that these are still there or not.
Mine no longer having any root, I grafted it for safety (I had already prepared a "tricho" ready for this operation) so I went on the safe side (or almost) and now vegetate quietly, moreover it produced some suckers that I detached and put to root and they also issued small trumpet flowers, very cute and fragrant
More than this I do not know what to say to help you, however, it would still seem in good shape and the only thing to do is to keep it under control and evidently if this "stasis" were to insist for too long it is appropriate to do what has been said above.