To the best of my knowledge such a pass does not exist for Europe as of now. This does not exclude its existence, but it is highly unlikely. Furthermore I doubt you would be able to make significant savings if there were such a pass, compared to careful price shopping.
Why I don't believe it exists
- Googling "Hotel Pass Europe" or "Hostel Pass Europe" does not return anything of the like
- I do follow miles & points blogs fairly closely and have not yet heard any mention of such a pass
- See also the comment and answer by @CMaster
What can I do to replicate the flexibility of such a pass
- Many hotel chains as well as booking.com offer rates that can be cancelled without a fee up until the day of arrival. You could book such flexible rates for every possible destination for every possible combination of days that you might spend there, and then cancel or use these reservations along the way. Do be careful though to cancel all of the ones you do not use, as otherwise you will be charged in case of a no-show.
- Buy hotel vouchers such as this one (no affiliation) and redeem them. Do however check carefully booking rules and make sure you will be able to use them all.
- Use miles & points programs. Many hotel chains have loyalty programs and offer to book rooms with points instead of cash (e.g. IHG). These can be significantly cheaper in case of events and still flexible rates. You might need to buy those points beforehand.
Honestly, initially I thought such a pass does not exist, as has been pointed out in comments by @ZachLipton
Hotels also use demand-based pricing to a much greater extent than trains. Hotel rates vary significantly depending on the market, the season, events in the hotel or around the city, occupancy levels, and other factors. A hotel chain wouldn't want to lock themselves into a single rate for all of Europe, as it would eliminate their flexibility to, say, charge a vastly increased rate if a major convention is taking up every bed in town.
However I did find such a pass e.g. for New Zealand. I did not on the other hand compare their pricing and I doubt you are making the best deal in terms of hotel quality and pricing compared to researching hotels and prices for every city without restricting yourself to one hotel chain.