There are two main failure modes for flourescent lamps.
1) breakage of the heater at one or both ends
2) cathode wear-out, wherby the heater is electricly intact, but wont emit sufficient electrons to light the lamp.
If the heater is open circuit, then most switch start or transformer start, or semi resonant start ballasts wont light the lamp. Such ballasts rely on a continous current path via both heaters for operation.
An electronic ballast, or some types of instant start magnetic ballast will normaly strike the lamp since they apply a high voltage to the lamp and dont "know" if the heaters are sound or not.
In the case of cathode wear out, then it depends on the internal circuitry of the ballast. A failing cathode will emit enough electrons to light the lamp provided that it is hot enough.
Ballasts that pass current continually through the heaters will often light a failing lamp. Alternatively runing the lamp on a higher output ballast may succeed, since the greater lamp current results in the cathodes running hotter.
It can be an interesting experiment to light a dead lamp thus, but I doubt that it is worth the trouble, remembering the very low cost of new ones.