Since this is classified as Tech/Engineering, I assume we are talking about a part of a machine (usually some kind of fuel injection system) which is called a reservoir (and not a large reservoir of water in the countryside where the term stub means something else).

As regards machines, the stub is a physical connection point usually welded onto a reservoir to which leads are meant to be attached.

Examples:
Hold overflow hose in left hand, push onto the stub if fell off of coming out the passenger side of the radiator fill spout. Refill radiator and reservoir to mark.
http://forum.miata.net/vb/showthread.php?t=309723

The invention relates to a connection stub to a housing, in particular a high- pressure fuel reservoir with a connection stub welded onto it,
www.patentstorm.us/patents/6513498/description.html

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Note added at 4 hrs (2008-12-26 10:37:03 GMT)
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In physics, although I doubt this is your application:
When a one dimensional (1D) ring-stub system is coupled to an electron reservoir, the states acquire a width (or broadening characterized by poles in the complex energy plane) due to finite life time effects. We show that this broadening is limited by anti-resonances due to the stub.
http://74.125.77.132/search?q=cache:-gbLkQSpWb0J:arxiv.org/p...