Will uncooked meat tenderise or toughen while stored in a refrigerator?
While dry aging does impact texture, storing a portion that you might purchase for yourself, or a small number of people, in the refrigerator for a few days will not impact the final texture.  Instead, consider purchasing high quality cuts, and the correct cut for your application.  Consider a tenderizing pre-treatment (some marinades are intended for tenderization).  Finally, of course, cooking process will greatly impact the final texture.