You can BUT you need to know the consequences:
1. Technically you are supposed to leave your apartment broom swept clean (no furniture) and the new landlord does have the right to charge you for removing it. If the new landlord received your contact information from your old landlord, that means they can contact you and possibly sue you.
2. If you don't want the furniture, your best method is to talk with the new landlord and ask him/her if they know anybody who wants it, or if they have any friends or contacts who can get rid of the furniture for you very cheap. Usually landlords know plenty of people in the industry. You need to work something out with this new landlord about the furniture because you never know, they may be able to help you later in your future.
3. I don't know but if your new landlord just purchased the building or house that you currently live in, this means your new landlord has a lot of new expenses and needs to find a tenant who can pay 3x your rent so this new landlord can recoup his/her investment. It's a business transaction. You don't buy real estate unless you can make money from it. Example: mortgage + property taxes + insurance + maintenance costs + water + garbage fees + utilities + labor costs + a small monthly profit = amount charged for rent. If your landlord doesn't have the rent to cover for these expenses = loss on the investment.
Hope this helps