setDate() has issues with month boundaries that are noted in comments above. A clean workaround is to find the date difference using epoch timestamps rather than the (surprisingly counterintuitive) methods on the Date object. I.e.
function getPreviousMonday(fromDate) {
var dayMillisecs = 24 * 60 * 60 * 1000;
// Get Date object truncated to date.
var d = new Date(new Date(fromDate || Date()).toISOString().slice(0, 10));
// If today is Sunday (day 0) subtract an extra 7 days.
var dayDiff = d.getDay() === 0 ? 7 : 0;
// Get date diff in millisecs to avoid setDate() bugs with month boundaries.
var mondayMillisecs = d.getTime() - (d.getDay() + dayDiff) * dayMillisecs;
// Return date as YYYY-MM-DD string.
return new Date(mondayMillisecs).toISOString().slice(0, 10);
}