I’ve given it a little thought and it’s hard for me to think of a suitable word. But maybe something here will stimulate you.
Most of the words used to “capture/trap” someone are negative or have such a connotation, e.g. abduct, acquire, attract, bait, beguile, cajole, capture, coax, decoy, draw, entice, entrap, grab, inveigle, lure, seize, take, tempt, wheedle.
I wonder if you should look to words describing why the user would choose to be captured e.g. affect, arouse, enthuse, entrance, excite, galvanise, induce, motivate, stimulate, sway, thrill, yearn
I like something like galvanise. It represents a sudden change but another meaning links to a longer term when we consider galvanised metal used for roofing. Where I come from it is mainly pre-colored and long run which is the word I’d use for the repository because you want long-term and persistent engagement in the long run.
Sway could be an acronym e.g. satisfy when a yearning, stay with and yield