A hospital in Bridlington is being wound down and staff morale is at an all time low, according to the union Amicus.
A union spokesman said patients and staff are being transferred to nearby Scarborough prompting fears that the Bridlington site is to close down.
But Alison Guy, chief executive of Bridlington, said staffing is at a "low level" but the site would remain open.
Managers at the hospital will now meet union officials to discuss morale.
Scarborough and North East Yorkshire NHS Trust is predicting a £2.7m debt at the end of the financial year.