Reeves said they had been looking for suitable accommodation but there was nothing affordable and she was uncertain what would happen when their notice period ended at the start of next month.
She added: “We’re just stuck at the moment and in limbo.”
The petition, set up by the former mayor of Ripon and retired Methodist minister John Richmond, calls on the trust to change its mind.
He said: “They’ve done nothing wrong. It’s more than unfair, it’s wrong.”
He said he hoped the campaigning would convince the trust and letting agent “to have a change of heart”.
Responding to the community support, Reeves described it as “incredible and really overwhelming”.
She added: “We can’t thank people enough, we’re truly grateful from the bottom of our hearts.
“It really does mean the world to us.”
In a previous statement, Robert Thew, chair of the trust, said: “Decisions about individual tenancies are taken by the Holy Trinity Properties Trust acting on the advice of our letting agents Linley and Simpson.”
In their previous response, Linley and Simpson said it did not comment on individual tenancies.
“As the managing letting agent, our role is to act on behalf of our landlord clients and, upon instruction, ensure legal notices are served in line with the relevant requirements.”
The BBC has contacted both organisations for a fresh comment.
