Should I buy a house with a title indemnification letter?

I'm in contract to purchase a house in Florida. I'm paying in cash. I've just been told by my realtor that there is a mortgage for the house from prior to the existing owner, which should have been cleared but somehow never was. In other words the title company which sold the house to the existing owner made a mistake. I'm told the current title company that is doing my closing will obtain a "title indemnification letter" from the previous title company. Is this safe for me to buy? Will I be at risk of this old mortgage, or have problems reselling the house? Thanks.