Families of residents at three Renfrewshire care homes are "concerned" at the proposition to close one.
The information was reportedly shared with those who may be affected two weeks before Christmas via a letter to residents.
The three council-run homes that are in consideration for closure are Renfrew Care Home and two Paisley facilities - Montrose Care Home and Hunterhill Care Home.
Many of those within the care centres suffer from dementia, with loved ones hitting out at the process of informing them - including emails landing in junk folders.
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Claims from family members say the information was sent to residents’ families/loved ones in an indirect manner via non-explicit email links.
Councillor John Gray, who covers Renrew North And Braehead, says that constituents have approached him expressing their concern.
Some carers/family members have also that receiving important information in their junk boxes is due to the name of the council's email which starts with "MBX".
Cllr Gray said: "I was first approached in December 2023 by families in my own ward who have relatives in Renfrew care home to be told they are closing one of three.
"They are being told the reason is to make up a £14.7 million deficit.
"And I was shocked at this news and the thought of moving these elderly vulnerable people.
"Also it was also brought to my attention about the lack of communication between health and social care and the affected families."
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Cllr Gray arranged a meeting with the head of social care along with the manager of the three care homes.
The Conservative politician said that it was confirmed one of three homes would close as it was to help bridge the huge gap in budget, however, no decision was made at that time regarding which home was to close as information had to be submitted to the Integration Joint Board (IJB).
A decision is set to be made on March, 8.
It was also stated that residents would be moved into homes that were identical to the ones that they are currently in.
In total around 134 residents live across the three care homes.
One family member of a resident said that they feel a move could "set back" their mum who suffers from dementia.
They said: "My mum was moved to another wing to allow for the flooring to be fitted and this distressed her when she noticed that the curtains were different.
"She found this very disorientating and distressing. Routine is important to how residents with dementia feel and any change, however slight, can set them back”.
Another concerned family member stated: "How will I visit? I currently walk to visit my dad and have no car.
"If he moves out of the town, I will need to take two or three buses to visit him. How can I do that as frequently and it will be costly, this is denying him the basic right of a visitor.”
A spokesperson from Renfrewshire Health and Social Care Partnership (HSCP) said: “The Integration Joint Board (IJB) agreed at its meeting in November that HSCP Officers should undertake a formal engagement process with our service users, residents, families and carers - as well as with our HSCP staff and any other relevant stakeholders - to gain a fuller understanding of all views around the savings proposals currently under review.
"This formal engagement process has been underway throughout December and more sessions have been arranged until the end of January.
“No decisions have yet been made on any proposals.
"Our engagement approach has been designed to give residents, families and representatives a choice in how and when they can contribute to the discussion while reflecting individuals’ needs.
"We have communicated with people in a variety of ways and have been updating individual communication preferences as part of this process.
"All views are being recorded and will be used to inform the EQIAs, impact assessments and final proposals that IJB Members will be asked to consider in March.”
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