What if the house is mortgaged to the bank when it is rented?

Mainly depends on the order of coagulation time.

If the mortgage is set first, that is, before you rent the house, the lessor has mortgaged the house to the bank, then the mortgage is superior to the lease right. According to the first paragraph of Article 66 of the Supreme People's Court's Interpretation on Several Issues Concerning the Application of the Guarantee Law of People's Republic of China (PRC): "When the mortgagor leases the mortgaged property, the lease contract will not be binding on the transferee after the mortgage is realized." Therefore, the bank has the right to unilaterally terminate the contract lease relationship, and you have no preemptive right.

If this causes property losses to you, according to the second paragraph of Article 2 above: "If the mortgagor fails to notify the lessee in writing that the mortgaged property has been mortgaged when leasing the mortgaged property, the mortgagor shall be liable for the losses caused by leasing the mortgaged property." You can ask the lessor to compensate you for your loss.

If the lease right is established first, that is, after you rent out the house, the lessor will mortgage the house to the bank. According to the rule of "buying and selling does not break the lease", the ownership of the house buyer cannot be opposed to the lease right, and the mortgage right has no priority over the ownership. Of course, the lease right can also continue to exist effectively against the mortgage right. According to Article 65 of the Supreme People's Court's Interpretation on Several Issues Concerning the Application of the Guarantee Law of People's Republic of China (PRC), "If the leased property is mortgaged by mortgage, the lease contract shall remain valid for the transferee of the mortgaged property within the validity period after the mortgage is realized." So your lease contract relationship is still valid.

It is worth pointing out that the mortgagee's mortgage right is the right of value, not the right of domination. What the law gives to the mortgagee is the right to be compensated first from the exchange value of the collateral, rather than the right to dispose of the collateral at will. Therefore, according to Article 230 of the Contract Law: "If the lessor sells the leased house, it shall notify the lessee within a reasonable period before the sale, and the lessee shall have the preemptive right under the same conditions." So when the bank auctions the property, you have the preemptive right, that is, you have the preemptive right at the same price.