They DID, they took samples from the "Elephant's Foot". The first samples were most likely taken during the 'Complex Expedition" that took place between December 1986 and early 1987, I think they blasted some samples off it with rounds from a Kalashnikov assault rifle, after attempts to chip some away with a hammer and an axe failed.
The 'Corium' from Chernobyl is known to have formed into six distinct masses below the level of the reactor's base plate, the 'Elephant's Foot' is just the most famous of these, and is black lava. There may be a mass of corium above the base plate, but I believe that is an unknown as this point, and it is possible that this does not exist! Three of these masses are black lavas, one is brown lava on a molten steel base, and the other two are brown lava covered by a porous ceramic material.
A lot of samples have been taken and analysed, (most after 1990 when it was discovered that the mechanical (physical) strength of the 'Corium' had weakened through radioactive deterioration. Many of these samples are held at the "V.G. Khlopin Radium Institute", where many scientific studies have had interesting results. Hydrofluoric Acid was used to dissolve some samples, this acid is known for it's ability to dissolve glass.
The coriums masses are different depending upon what the fuel melted and combined with, and studies suggest the fuel reached above 2,600 °C BEFORE the explosion, and fuel at these temperatures melted into the Zirconium alloy fuel cladding and combined with steel from the pressure tubes and the sand from the outer circumference barrier (which formed into a strange glass ceramic). Accident mitigation measures also dropped boron carbide, sand, lead, clay, and dolomite into the open reactor, and I do not know if any of these additives contributed to the corium's constitution.
It appears that the reaction was ONLY really stopped when Liquid Nitrogen started to be introduced into the reactor space on May 5th, this had a significant thermal cooling effect within 24 hours, the nitrogen acted as an oxygen blocker too, and May 6th showed a sharp reduction in the release of radionuclides. It took 9 days to really bring the runaway reaction under control.