Six care homes and four day centres are to be shut by Leeds City Council.
But union GMB is resisting the plan and has called on the public to take action during the 12-week consultation.
Regional officer Jon Smith said: "Leeds City Council has begun a 12-week consultation from March 11 on closing six care homes. Consultations are also under way on four council-run day centres.
"GMB will seek on behalf of its members to keep all the council-run home and day centres open and properly funded.
"Staff are dedicated and have many years' experience.
"This will be lost at the stroke of a pen, while the residents and service users will be sent packing off to the private sector."
He said that three homes which closed last year, and others closed earlier, stand empty "with no known plans to be used for anything else.
"This is money being sat on that could be reinvested into the homes and day centres," he said.
Mr Smith pointed out that the closures are estimated to save £5 million but that the annual saving is only £800,000.
"The whole of Leeds will be affected in some way by these cuts but we are unsure if all Leeds residents are aware of this.
"We should be investing in public services and not selling them off to the highest bidder with a priority to make money.
"The people of Leeds have got a very simple choice - care or profit.
"GMB want them to tell the council where they stand during the consultation."
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