My mom and grandmother made something similar. My grandmother's recipe is:

Dissolve 3/4 cup pickling salt in 1 gallon warm water. In a crock, layer a good amount of cucumbers (she left them whole, but slit them through the middle so the brine would get into the center), a generous amount of dill and garlic cloves. Cover with the salt water solution and place a piece of rye bread on top. Leave in the sun for a least 5 days (cover with cheesecloth or a tea towel to keep out the bugs). When satisfied with the taste, put them in the fridge with the strained brine and some fresh dill if you want. I do love these pickles, and still make one batch a year to keep the "tradition" going :-) I don't can them - refrigerator storage only, but they do keep for quite a while. I add some vinegar to the brine when storing, but I like "vinegary" pickles.

Linked below is an old thread about these types of pickles as well.

Here is a link that might be useful: Sun-Fermented Dill Pickles

Thank you, Malna for the link. I did not realize this was what is called a fermented pickle. That link pretty much tells me all I need to know.
Carol