I'm going to assume you mean in the United States...
Mailing a letter does not always require a return address as you understand from your question.
A return address must appear legibly on:
- Mail of any class bearing a printed ancillary service request (i.e. "Return Service")
- Official mail
- Mail paid with precanceled stamps
- Matter bearing a company permit imprint
- Priority mail
- Periodicals in envelopes or opaque wrappers
- USPS retail ground
- Package services
- Parcel Select
- Registered Mail
- Insured Mail
- Collect on Delivery (COD) Mail
- Certified Mail (if a return receipt is requested)
- Priority Mail Express
- Detached Address Labels and detached marketing labels
- Adult signature required
Given that if your mail was not any of the above, you could make up an address and then make it illegible so that it cannot be read (using a pen or marker, or white-out to obscure the address). Do not keep a legible address that does not belong to you as the return address.