The Puppy Dog Close: let them take the pup home first and say bring it back if they change their mind.
Book: The 4-Hour Workweek
In the book The 4-Hour Workweek, Tim Ferriss introduced this term as "The Puppy Dog Close in sales is so named because it is based on the pet store sales approach: If someone likes a puppy but is hesitant to make the life-altering purchase, just offer to let them take the pup home and bring it back if they change their minds. Of course, the return seldom happens. The Puppy Dog Close is invaluable whenever you face resistance to permanent changes. Get your foot in the door with a “let’s just try it once” reversible trial."
In sales, The Puppy Dog Close can be generalized as letting customers take the product home on a trial basis first. Nevertheless, in the book, Tim Ferriss further used this technique and elaborated how he negotiated with his manager to avoid attending most of the meetings in the company, which he thinks are just a waste of time.
He said things like "Can I sit out just for today? I’d be distracted in the meeting otherwise. I promise I’ll catch up afterward by reviewing the meeting with Colleague X. Is that OK?" He persuaded his manager to "let’s just try it once" and proved that nothing bad actually happened. Therefore, he then repeated this routine and ensured that he achieved more outside of the meeting than the attendees did within it.
I first learned the term in the book, but you can also learn more about this in the article Model the 'Puppy-Dog Close' Technique.