There is a different thread on this very idea, which was submitted two years ago. Can you click on thumbs-up Vote Up icon? Voting makes the difference, not so much comments. 
Link: Re: Unplublish form
Hey Hubspot, maybe about time you make such a simple feature available? We’ve all been asking for it in this thread for a year. Do we need to get on our knees and beg for it? So many simple and necessary features have been requested in so many threads and they should be the one you must focus on in Q1 2022… Listen to your users ASAP
We absolutley need an unpublish or expiration date option for forms. I would consider this critical.
Unpublishing a form would be so helpful. We run surveys that have deadlines and have no way of stopping people completing the form after the cut off date. It would be so useful for this functionality to be added.
How is unpublishing a form not possible on this platform? Mind blown. 
Upvote given! Surprised to see this original idea was submitted close to 2 years ago. We need this functionality HubSpot! Thanks
In 2022, I wanna unpublish a form please.
I would like this feature to be added as well. It is cumbersome to have to update the form with a message that it is closed or have to clone and delete it.
This is a frustrating oversight. We would like the ability to disable or put time perimeters around some of our forms. Many of the forms we use are only relevant for certain events which are time sensitive. We are newer to HubSpot and this is a very disappointing discovery.
673 days, 121 upvotes and counting.. C’mon Hubspot.. 
please this is a good idea
Unpublishing a form should be a basic feature in this platform, along with exporting clean html email for a third party partner.
Yep, big upvote from my side. Use case is that we’re hosting a graduation event, and have a cut off date for RSVPs.
However, people can still share our form with others and submit — only to then not get a reply/be disappointed.
+1 to this simple request.
Yes, this would be amazing! I have many of these forms that I would need unpublish but would need the data. I hope this gets implemented soon.
Agreed here. Similar to how workflows can be turned on and off, it would be helpful to have the ability to turn on and off forms. Thank you!
This is an important feature for us. We use the form for event registrations and there is an attendee cap. We’ve had people register after the landing page was unpublished but they had access because we didn’t want to delete the form and lose the data! Unpublishing forms is a much needed functionality!
Yes, this is a great idea and is much needed! I have customers who continue to use old links to old HubSpot forms. I don’t want to just delete the forms because I don’t want to lose that submission data that’s stored all in one place. I know HubSpot workflows can be unpublished or turned off so they are inactive. It would be great if there was a simple button to just make the form inactive so that customers can’t continue to use it. I’ve let our customers know to use our new internal links, but they don’t always remember/understand and still use the old HubSpot form links they have bookmarked.
I think it would be very helpful to unpublish a form. You might want it closed for now, but want to keep all reporting that goes with the form.
BIG need!! Our website is not hosted on HubSpot so I need to be able to truly see that a form is unpublished to ensure there is cross visibility. Another option is to archive so that analytics are retained.