During the financial crisis a number of distressed banks were rescued by the public sector injecting funds in the form of common equity and other forms of Tier 1 capital. While this had the effect of supporting depositors it also meant that Tier 2 capital instruments (mainly subordinated debt), and in some cases Tier 1 instruments, did not absorb losses incurred by certain large internationally-active banks that would have failed had the public sector not provided support.
So it wasn’t just senior bondholders who were bailed out: in some cases, junior debtholders, pref holders and even equity holders got a degree of taxpayer support, which is pretty wild. This is the sort of thing that happen in a crisis, when you don’t have a proper resolution regime (but you do have banks that own each other’s debt or near debt).
In the Glass-Steagall/FDIC world, bank resolution is done briskly and proactively: the bank is nationalized (yes, Virginia) and dismantled; operationally, it never misses a beat, and depositors are protected. Without an FDIC and its supporting legislation, it all gets messier, though. If your bank has to go bust before bondholders and depositors are tackled about the losses they are to take, then you will get bank runs. See Northern Rock, RBS, and it now seems, Dexia; see also the plight the Irish landed in, once their government decided it had to ward off a run by guaranteeing both depositors and bondholders.