@Angela Russo I'm guessing that it is going to be extremely difficult to locate a chart identifying states that allow fractionalization without securities law and brokerages coming into play. That sort of information is going to be internally controlled by a law firm with a practice focusing on notes. Given the size of the market for fractionalizing notes of the kind BP members are interested in, you're looking at smaller law firms which likely won't have conducted any sort of 50-state survey. At large law firms, 50-state surveys are saved for the summer associates and cover a myriad of areas, but 50-state surveys become less and less common the smaller the firm gets as the firm will focus on more niche practice areas and geography.
Regarding a borrower refinancing or selling the property: I cannot speak to the normal practice that @Marco Bario may be able to address, but this situation should be clearly addressed in the agreement between the original note holder and the party taking the partial interest (whether through assignment, fractionalization, or whatever method is used). My guess is that the party taking the partial interest would be paid out the amount owed under the agreement with the original note holder retaining the rest. For example, if I purchase 24 months of $500/month payments, my guess is that industry standard is to agree that the party acquiring the partial interest would take a lump sum payment of $12,000 minus the amount already paid when the note is refinanced or the property sold -- essentially an acceleration clause of sorts.