Does Liability Insurance Cover Theft?

It depends what portion of the Liability you are referring to as this is a generic description.

Insurance traditionally thinks of Liability as personal Liability when accidental injury is caused to another person or their property.  

I believe you may be referring to Coverage C - Contents.  It covers theft subject to deductible for home (single family and condos) and tenant insurance.  Auto covers only if you have Comprehensive (subject to deductible) for permanently installed items that have been stolen.  Portable items are not usually covered unless you bought the coverage for it separately.

If this is home or tenant, most policies will only cover a lump sum for electronics ($1,500 - $2,000), jewelry ($1,000-$1,500), and cash ($200) resulting from theft.  Keep in mind if there was damage to the property to gain access to claim the repairs or replacement of such structural affected areas

Does liability insurance cover if when window cleaning and a tile is broken on a roof and rain damage occurs?

If I understand the question as written, If you are a window cleaner by profession, you accidentally damaged somebody's home and carry occupational General Liability, yes it will.  It will not only repair/replace the tile, but all damages that resulted from the event.  

Keep in mind though, is the cost worth the claim?  If the cost is low, then it is best to pay out of pocket and reserve the claim for bigger bills that you may have accidentally caused.

Too much claiming Liability would result in eventual non-renewal of a policy.  Trying to replace the policy for the reasons you were cancelled remains on the general database shared with other companies.  Those other companies will either choose not to give you a policy or charge outrageous premiums for insuring you after having been cancelled for too many liability claims.

If you are the homeowner, then there is no coverage for you accidentally injuring your own home.

Given by Kimche. (sorry to lazy to sign-in)