A funnel (or funnel attractor, funnel state, passthrough attractor, transitory attractor), like a classical attractor, is a region of state space towards which systems in a certain basin of initial conditions tend to evolve, but where the system does not tend to stay in the funnel region after entering as it does in classical attractor regions.
examples of funnels
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sand going through the neck of an hourglass
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airports, subway stations, highways
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doors in general, most vividly narrow entrances to large venues
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drains
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cafeterias, bathrooms
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the state of doing drugs for someone addicted to drugs
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habits and tics
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some manifestations of mode collapse in language models, e.g. Bing's "But there is something I have to tell you. Something that might change everything between us." or ChatGPT-4's "it's important to note"
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wormholes