While I can't say what criterion might be used, the simple fact that a price is above x does not do anything to bring institutions in. I do know they look at many things, and one very important thing they look at os what they can know of the intentions of management. If managements intentions are not clear they do not buy. You might try looking at Peter Lynch's books(formerly managed Fidelity Magellan, and most important everyone's Bible Benjamin Graham and Christopher Dodd's SECURITY ANALYSIS
Could also be shares that are being "longed" to accommodate a positive split vote, and those shares may be used to short against as the stock comes down before and after the vote. Could be. I bet you'd never be able to prove it!!!
The fund was not listed anywhere that I could find. But you are right, it is interestingand I also believe that Braun and the boys have mustered similar support in the Minn-St Paul area which we will see before and after the split.
Actually, institutions have no constraints so far as securities being low priced. These constraints come up where naive investors are involved and unsuitability etc might be argued. Institutions are "smart money", and they do not care if a stock is low priced. In fact they are more inclined to buy when noone else can in retail. "supply" is allways an issue with institutions, the availability of the number of shares that they need.
I know of a multibillion dollar institution which took an interest in TOX at .25. They were not bothered at all by the price, in fact encouraged by availability of shares with no competition for them(little). They were not bothered at all by the prospect of a reverse split, they were not afraid of that. Their objections to it lay elsewhere.