Well this is one of the conclusions of those experiments detailed in the Tawfik papers discussed in Miller: Axe Decisively Confirmed? thread. This one in particular: http://www.ira.cinvestav.mx/portals/0/Estudiantes/Tokuriki_2009.pdf
In the absense of purifying selection, mutations in protein coding genes that affect amino acid sequence will quickly degrade protein stability. Generally, the conclusion of the paper is that evolved proteins have some “threshold of stability” where they can initially tolerate some accumulation of mutations, but once this threshold is exhausted, the vast majority of mutations negatively affect protein stability and thus function, and become significantly deleterious for that reason.
If what you’re saying is really true, it should generally be the case that mutations in proteins are just as likely to enhance stability, as to degrade it. But that isn’t what is observed. The key player here is purifying selection against stability-affecting mutations.