A black hole, in the theory of general relativity, can be composed of any mass. If the mass is low, the higher the matter's density has to be in order for a black hole to be created. There are no known processes that can produce black holes with mass less than a few times the mass of the sun. If black holes that small exist, they are most likely primordial black holes.
Without becoming a black hole, the maximum mass that a neutron star can possess is not fully understood. In 1939, it was estimated at 0.7 solar masses, called the TOV limit.
In 1996, a different estimate put this upper mass in a range from 1.5 to 3 solar masses, until twenty years later, when it was determined that anything more than 2.16 solar masses becomes a black hole after a supernova occurs. Most neutron stars are between one and two solar masses, while most black holes discovered are determined as being four solar masses or above.