Although the rulebook allows for their entire season's results to be expunged, the more likely option is that the Scottish Professional Football League board would decide to apply automatic 3-0 wins to all of their very last opponents.
Liquidation is the worst case scenario, but a growing fear for everyone involved. Insolvency expert Bryan Jackson yesterday admitted the club was at its "lowest ebb" after nine months in administration.
Rule C53 in the SPFL rulebook gives the governing body's board the power to expunge a team's results for a whole league season but that would cause major organisational headaches and is considered very unlikely so late in the season.
It is more conceivable that the eight-man SPFL board, headed by independent chairman Ralph Topping, would agree to let Hearts' results stand and award 3-0 wins to any end-of-season opponents they are unable to face. Hearts will be relegated if they lose at home to Aberdeen tonight, and then have six games left to play.
There has been a lack of communication and information from Lithuania which has deeply worried Jackson, of insolvency firm BDO, potential owners Ann Budge and BIDCO and the Foundation of Hearts who intend to eventually take the club into fan ownership.
A meeting at which creditors of Ukio Bankas and UBIG may vote to formally pass the £2.5m Company Voluntary Arrangement (CVA), and transfer the shares to those in Scotland who wish to save the club, is now due to go ahead on Monday. But it has been postponed several times already and any further stalling could push Hearts over the edge.
The situation has become grave because Hearts have money to survive only until around the end of April. Even if the CVA is agreed in Lithuania on Monday, an automatic 20-day appeal period pushes the club's uncertainty to April 27. The SPFL Premiership season ends on May 10.
What worries those trying to save Hearts is the lack of an explanation for the repeated delays in Lithuania. If the creditors there are holding out for more than the £2.5m on offer from Scotland, they have yet to say so.
"This recent set-back has really hit us and hit us very hard, to the extent that this is probably the lowest ebb we've ever got to," Jackson said. "This deal should really have been over the line. We have to accept there is a threat of liquidation and we are doing everything we can to avoid it.
"It is in absolutely nobody's interest - whether it's a creditor or a shareholder or a supporter - it can't be in anybody's interest, it just doesn't make any sense, and this is what we are struggling with. We just have to make sure it doesn't come to that."