The operator who took the call judged that that the woman's situation wasn't urgent and thus elected not to dispatch an ambulance to her home, the local Dala-Demokraten newspaper reported.
Instead, the operator called an elderly couple living nearby and asked them to help the woman instead.
However, the couple were unable to find the woman's apartment and eventually returned home without helping the woman.
"The whole incident is very unfortunate. This operator has acted entirely of his own accord," said Daniel Lundin, manager of SOS in Falun, to the newspaper.
The daughter of the elderly couple who unexpectedly found themselves tasked with responding to the emergency services call was furious over SOS Alarm's actions.
"How can SOS call people late on Saturday night and call them out on duty?" she wrote in an aggrieved statement, wondering what might've happened if her parents had injured themselves trying to help the injured woman back on her feet.
"Might they have been charged with breaking and entering?"
In the end, the injured woman was helped by another neighbour, and was finally able to get back up.
Lundin explained that how to respond to the injured woman's call for help is complicated by uncertainty about how serious the situation may be.
Depending on the severity, he said, responding to such calls may instead be the responsibility of home care services rather than emergency services.
The incident is the latest in a number of cases in which SOS Alarm has come in for criticism.
Earlier in the week, a woman from Söderham in eastern Sweden who was suffering from heart disease was made to wait more than an hour for help because SOS Alarm operators sent the the ambulance to the identical address in Hudiksvall, a town 50 kilometres away from where the sick woman lived.