The offer closed yesterday to raise funds with Hearts pleading with fans for support over their myriad of financial problems.
The scheme was launched in late October and designed to raise £1.79m, leaving Hearts short of their target.
Four thousand supporters signed up to the scheme, Hearts said, but there remains a shortfall of almost £800,000.
Hearts, at the request of supporters, will continue to accept completed applications and payment up until the conclusion of Sunday's Clydesdale Bank Premier League match at home to Dundee United and say the figure of £1.05million raised - through the share issue scheme and other fundraising - may rise.
Seven days before the deadline - the most recent update - Hearts revealed more than £800,000 had been raised and urged fans to sign up or that the club could face another do-or-die situation after averting a winding-up order earlier this month by paying a £450,000 tax bill.
Hearts settled another issue with Her Majesty's Revenue and Customs by agreeing to pay £1.5million over three years.
Players voluntarily deferred their wages last month but they were paid before receiving their full salary for this month on December 16.
Hearts warned the club's position remains precarious and supporters have been urged to continue to attend matches in high numbers in a bid to reduce the near £800,000 shortfall.
Hearts raised £161,000 in "unbudgeted" ticket sales from the matches at home to St Mirren, Celtic and Aberdeen. Hearts director Sergejus Fedotovas said fans had "given the club a lifeline in its darkest hours".
Fedotovas, right-hand man to majority shareholder Vladimir Romanov, said on the club's official website: "There is still significant work to be done but this time there is a tangible focus that simply involves fans getting back to what they do best and that is supporting the team at Tynecastle in great numbers.
"We will continue to raise funds through our donation telephone line and online through the club website as well as encouraging more fundraising events. However the best way that we can all push through this difficult situation is by supporting the team and buying half season tickets and match tickets.
"Together we can emerge a leaner, stronger football club and I expect that the supporters will be the ultimate beneficiaries as we progress towards making Hearts a club that is one of the most progressive and supporter-centric in the country."
When the share issue scheme was launched the prospect of supporter ownership was mooted. Discussions are continuing.
Fedotovas added: "We are now halfway there and our work must continue. With your support and only with your support will this club survive and thrive.
"With this in mind we have progressed discussions with Supporters Direct, the official recognised Government-backed organisation, in order to establish how best Hearts supporters could take their club forward.
"We are now working on the most suitable model that will give the club the best long-term chance of development under true supporter control.
"We expect to announce further details of this in the early part of 2013."