Actually, you'll probably find that the solicitor went through the whole process with them, advised them just how much trust is needed in these situations, probably advised them that closing dates are aspirational only but that if purchasers are now serious that its better to take the money and run and therefore fixed on the early closing date requested, that contracts are signed and binding but that if purchaser delays that there is a further 28 day period when a completion notice has been served and run before vendors can choose to take deposit and terminate contract or opt to try and enforce the contract.
If you believed a lot of what you read on this board, conveyancing could be done ( probably better) by a monkey than a solicitor, all ( well, nearly all) solicitors are rubbish and it should be possible to press a button and do the whole process automatically. In reality, it is primarily the clients who make things complicated, as here, the purchasers appear to be behaving very badly.
mf