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Staff at Maidstone Hospital were invited to apply for redundancy
Just 50 staff members have applied for voluntary redundancy at the Maidstone and Tunbridge Wells NHS Trust.
The figure represents only 1% of the trust's 5,000-strong workforce.
The trust wrote to staff last month asking them to consider applying for redundancy before October 5.
It is looking to save £15-20million every year for the next three years.
The low response raises the possibility that forced staff cuts may follow.
Bosses previously signalled that if desired savings cannot be made, compulsory redundancies may be considered.
A trust spokesman declined to comment on whether the 50 applications were disappointing. The trust has always stressed that not everyone who applies to leave will be granted their wish.
The spokesman added: "The trust will now look at each application in turn, in detail, to see if the application is in line with its policy of not having any impact on frontline patient care."
Those who are successful will leave the trust by January 31.