Not like the picture. The rope was more to stop you falling off the bench where you were sitting up asleep.

For an extra penny [than a one penny sit up] you could pay to sleep literally hanging over a rope. This was possibly marginally more comfortable, as if you fell asleep the rope would prevent you from slipping onto the floor or head-butting the bench in front of you.

https://www.historic-uk.com/CultureUK/Two-Penny-Hangover/

Edit - none of the sites mentioning it have any sources. The closest to a source I’ve found quickly is this passage from Dickens Pitwick Papers, which to me doesn’t sound like the arrangement as described in the photo but perhaps something more akin to hammocks. Especially given the part that says “down falls the lodgers”

And pray Sam, what is the twopenny rope?’ inquired Mr. Pickwick. ‘The Twopenny rope, sir,’ replied Mr. Weller, ‘is just a cheap lodgin’ house where the beds is twopence a night!’ ‘What do they call a bed a rope for?’ said Mr. Pickwick. ‘Well the advantage o’ the plan’s obvious. At six o’clock every mornin’, they lets go the ropes at one end, and down falls all the lodgers. Consequence is that, being thoroughly waked, they get up very quickly, and walk away.’”

This site https://www.geriwalton.com/victorian-four-penny-coffins-penny-beds-homelessness/ says that the coffins were actually 2 pennies, or 4 with a meal. So why would someone sit over a rope for the same price? Again a hammock type arrangement here seems more logical to me.