The owner of the property is responcible for the tax to the officials UNDEPENDING of if the unpaid tax is from before or after the transfer was done.
If you can demand the tax from the sellers is an other question. What do the sale contract say concerning tax?
Undepending of what the contract says, it can me hard to get money. That's why tax, title transfers and such better be done before/at the same time as transfering (some of the) pay for the property, so costs and depts can be cleared.
The rest I don't know, but I asume it's possible to go to court to get the title transfered by proove your part of the deal is done,
BUT such take long time, so better if you can make the heirs agree to transfer. Perhaps you can reach a compromise, if they don't agree it's their tax to pay. If you can't reach an agreement concerning the tax, then it's up to you if you want to go to court or pay the missing tax. Or you can try to skip to pay the tax (now) as rather many property owners do
¬† IF it isn't demanded to get the title transfered, but then it will be your dept to RP. (=You sign a document to the selling family saying it's your tax dept, in exchange for they sign transfer the title, NOTE! make sure ALL needed sign the transfering to avoid such risks for problems in the future.)