It might be useful to define what exactly you have in mind when you use the term "solitary" (or if you have something specific in mind), but yes, it's possible. For example, red foxes (Vulpes vulpes), or better said, their melanistic form (silver fox), have been experimentally domesticated since the 50's in Siberia. (A really fascinating research, not only because of how long it's been going on, but also because of its genetic and genomic results, insights into neural crest function, et cetera.) Furthermore, it's important to note that domestication may affect the mating system and social behaviour of the domesticated species. E.g. the wild predecessors of some now polygamous domesticated animals were presumably monogamous.