I mean if every variable aligns with any possible edge case that can bleed off velocity including three body interactions with the moon. Is there ever a situation where some substantial (car++) or enormous (skyscraper+++) size rock lands on the surface without explosive energy? Align stars, consult math mediums, play some ZZ Top, piss off Bary the narcissist, or conjure a primordial black hole, just land me a big rock in my yard Science Santa. I want an m-type for Maymass, but any type will do if you can land it.
Yeah, with a Lagrange keyhole orbit past the Moon (which is what OP is asking about, not just plain escape velocity), you could park an Asteroid Belt asteroid in an orbit around the Earth. But it will be a high orbit. Not sure how low you could get it, I’m hoping a circular geostationary orbit is possible? But more likely something in the 300,000km range.
Low orbit is out of the question. Maaaybe you could park the asteroid in a highly elliptical orbit where the perigee is inside the atmosphere. The drag will circularize it if the asteroid is small enough. But not so small or weak that it burns up or breaks up before that happens. And not so big that drag takes too long and the orbit wobble makes it hit the surface. In a low Earth orbit you now only have 8km/s delta-v to deal with.
But to get the asteroid to gently touch the surface the way OP describes it, like some sort of skyhook? Is impossible short of a planet X or a rogue black hole passing even closer to the Earth than the Moon at the right moment. And whatever remains afterwards would be hard to call a surface: https://www.youtube.com/watch?v=kRlhlCWplqk