Hoople Ltd is providing items such as shower chairs, toilet frames and hoists while Careium UK is taking over technology services including lifeline units, fall detectors and emergency call monitoring.
The council said people who use those services did not need to take any action or change their routines or equipment use.
They were, however, advised to make a note of new contact details for the companies, external.
Hilary Hall, corporate director of community wellbeing, said the council worked quickly as soon as it became aware of concerns, adding: “We have found new suppliers who can pick up these services immediately with minimum disruption.”