Yes there is one that supposedly emulates the sashiko stitching which I happen to love, however they are quite pricey.:)

I don't know... I DO have a special stitch on my Janome (Memory Craft 4800 Quilters Edition) where you use monofilament on the top and thread in the bobbin and it looks like it skips a stitch and looks JUST LIKE hand quilting.
I never use it. lol See, I'm afraid of the long lasting effects of monofilament thread. Will it last over time. Also, it takes a LLLLOOOONNNNNNGGGG time for the stitching. Creeps along.
That's all I know about what you are asking.

I saw a Singer on HSN yesterday that has a stitch that looks like hand quilting. I was tempted to buy just to get that stitch, but I was good and didn't buy it.

My brother CS6000i has the stitch and it wasn't an exensive
machine.

That is why I bought MY machine, just for this stitch. I bought it back in 2003 and only made ONE small quilt with that stitch!~ so, don't buy a machine just for this stitch, if you were to ask my opinion.
(Now, lucky for me, I like my machine and still use it dailly .It's my ONLY machine. So, for me it worked out. IT's a Janome 4800 Quilters Edition.) Mine, it's very slow to do this stitch. It has to go forward, then backwards, it is almost double the work in sewing the stitch. Also, I'm not a fan of monofilament , not knowing over time what it will do. 20+ years down the road, will it begin to break apart,etc?

my Bernina 180 has a hand quilt stitch. uses clear thread (only one) on top and colored on bottom. Very very nice...have used it many times

I have the Sashiko machine and mainly use it for smaller projects but I really do like the stitch on it.

I have a Viking Rose that has a handquilted stitch. You us a white or color in the bobbin and clear on top. I have only use it on small projects so far , but it does look good.

Have any of you used the "2 hole needle" for this? Just bought one but haven't tried it yet. Would like to know. Sounds like it would work also.

I have a Sashiko - it's by Baby Lok and is the perfect partner for my Baby Lok Symphony - Have hand quilted anything since I got it. I love the look it produces.