Every jigsaw I’ve ever used was a hand tool and had the blade held at only one end. What you’re referring to sounds like some kind of precision bandsaw.
There are manual jigsaws which are similar to a coping saw, handheld power jigsaws similar to a sabresaw, and table jigsaws as Chronos describes. All are reciprocating saws. Bandsaws can have very narrow blades, as little as 1/16", but those blades have a limited life. A table jigsaw, like a manual jigsaw, can have a very narrow and thin, but strong blade because it is under tension from both ends.