Hope I am not too late:
Been there, done that. As others have stated, they might not have the right insurance and will have to pick it up for you. If you have to pay for it why are you working for them? At that point you are a consultant. There is a question on the PL policy application that asks what % of your business is from a single source, there is another questions if the company applying is a contractor. They will have a tough time answering those questions which is why they might set you up independent from them... but at that point you have lots of risk but very little reward.
One other thing to note, be very careful about the tail policy. If the company goes out of business and decides not to pay the policy anymore do you want to be "left with no protection"? This was a huge sticking point when my previous employer went out of business (a steel fabricator). Luckily I have leverage and used every ounce of it to my advantage. If I hadn't they would have told me to pound sand and I would have been on the hook for 1/3 of my yearly salary to pick up this policy (they never negotiated right when shopping for policies).
Finally, if you except the job be prepared for the "we screwed this up now you have to justify our screw up" projects. Those are only fun if they respect your opinion (been on both sides of those arguments).