The Stephen Joseph Theatre in Scarborough was set to close in September, with the loss of 30 full-time and 60 part-time jobs, after North Yorkshire County Council axed a grant of nearly pounds 80,000.
The grant was linked to pounds 175,000 Arts Council lottery funding and the theatre, which opened a year ago with financial backing from the playwright, would not have survived the loss of so much cash.
But yesterday the council announced that pounds 40,000 may still be available for the theatre if certain conditions are met.
Although the cash only amounts to half the original grant, it means the theatre - which must produce a "viable business plan" to get the reduced sum - will still receive all the lottery money and should therefore remain open.
Theatre spokeswoman Jeannie Swales said: "We're very pleased that the council has re-addressed the funding issue, but we're not throwing any parties until we know for sure what's going on."
The council, which has said another pounds 30,000 could be available for the threatened Harrogate Theatre, has warned that a newly elected county council will be responsible for awarding next year's grants.
Miss Swales added: "We're not completely in the clear - we'll have to do revisions of the programme and budget now.
"The future is much much brighter than it was a week ago, but it's still not fully assured."
The theatre, which is named after Sir Alan's theatrical mentor, stages the playwright's new productions before they go to the West End theatres in London.Reuse content