Yes, they are still out there, but most are not the same as the older AYH and HI hostels were, and the coronavirus crisis probably isn't doing a lot of them any favors. . Most are 'private' businesses and have the traditional shared 'bunk bed' accomodations, bathroom facilities, laundry room, and individual lockers, but it varies from there. Some charge for bedding, meals are extra (but there's usually a shared kitchen), and some require you do some participatory work (wash dishes, linens, etc). Clientele can vary considerably from nice to nasty.
The last time I stayed in any were two in 2016 in Santa Barbara and Hermosa Beach in California. The Santa Barbara one was basically a somewhat isolated wing of a hotel where the rooms were converted into 'bunk bed' arrangement with a bathroom for each room. The one in Hermosa Beach was more traditional. I also stayed in one in a house not far from the Amtrk station in San Luis Obispo that I liked a lot, actually stayed there on two separate trips. A lot of the newer ones can be found on Booking.com.
I've got more income these days so use a lot more motels.hotels while on the typical 3-7 day tours I like to do.