The offer closed on Wednesday 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.
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 raised £161,000 in "unbudgeted" ticket sales from the matches at home to St Mirren, Celtic and Aberdeen. Hearts director Sergejus Fedotovas, right-hand man to majority shareholder Vladimir Romanov, said fans had "given the club a lifeline in its darkest hours".
Fedotovas said on the club's official website: "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."
When the share issue scheme was launched the prospect of supporter ownership was mooted. Discussions are continuing.
Fedotovas added: "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."