I have encountered this situation. You are correct, investing in a company with 50% dead equity is unattractive. This is a "case-in-pint" showing why vesting agreements are important from the beginning.
Several pieces of information are important:
--How old is your company and what was the co-founder's contribution to date? There is a big difference between a 10-month contribution and a 10-year contribution.
--What is your relationship with your co-founder? Is he/she amenable to doing what is best for the business?
--If you need investment to be successful, this can be a lever. Unless the co-founder is cooperative, you'll close the doors and move on. He/she will get nothing.
--What assets belong to the business? Can you close it and simply open a new business on your own?
Hope this helps.