Clyde will be playing in the Second Division next season
Clyde have asked manager John Brown to step down and aim to terminate the contracts of all full-time players.
The Cumbernauld club are preparing for life in Division Two next season and have been dogged by financial problems.
Clyde were recently threatened with eviction from Broadwood Stadium after failing to pay rent.
Chairman Ian Letham told BBC Scotland he was optimistic about the future but he admitted: "Every club is in danger at the moment."
Clyde are dealing with a shortfall of around £100,000 and see no option but to turn part-time for the next campaign.
However, Brown, who has a year of his contract to run, is reluctant to leave his post after being offered one month's pay to go.
The burden of responsibility as to the future of the club as been placed on them and that's unfair
PFA Scotland chief executive Fraser Wishart
The Bully Wee faced a deadline eviction from Broadwood Stadium on 26 April over unpaid rent debts of £140,000 but an agreement was reached with the local council.
Clyde's directors agreed to reduce rent arrears by £40,000 immediately, with the remainder to be paid over the next 19 months.
PFA Scotland chief executive Fraser Wishart told BBC Scotland the players and staff should be given more time to consider the news, but sympathises with Clyde's plight.
"All clubs face problems and relegation adds to that," said Wishart.
"It's happened very quickly and the players feel they've been pushed into a corner, they've been given two to three days to make a decision.
"The burden of responsibility as to the future of the club as been placed on them and that's unfair."
A statement issued by the club read: "The recently reported financial difficulties of the club have not gone away. Much of the budget deficit for the season remains and confirmation of relegation last week added to the financial woes.
"The club has been in discussion with players and other stakeholders to avert an extension of the financial crisis.
"The positive outcome of recent talks with the stadium landlord gave the club time to finish the season in an orderly manner at a time when limited prospects of staying in the First Division remained, now that the season has ended and relegation has been confirmed the club requires to readjust its cost base to survive in the Second Division.
"This morning, the players were all asked to attend a meeting at the stadium where they were brought up to date with the current position, the manager was similarly briefed by directors on Monday.
"During these discussions, the club revealed that all contracts would require to be reviewed or ended to allow the club to restructure for next season at a fraction of current levels.
"Efforts continue in the business community and elsewhere to find additional backing for next season, but following a disappointing season on the park and the effects of the economic downturn off the park the board has had to acknowledge that the prospects of finding adequate additional funding to maintain the current squad are very low, in the absence of any significant support then the cost base of the club has to be reduced.
"The next few weeks will be an uncertain time for Clyde and all involved around the club would like to thank everyone that has contributed to the Back the Bully Wee campaign to date. We would ask that everyone keeps the momentum going and do what you can to help us pull through."
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