It would really depend on a few things
-what is the size of the mortgage owed on the property?
-does the owner need to move quickly?
-what is their monthly carrying costs
A cash offer not only makes the transaction smoother but can offer a key component which is time. A seller may more inclined to take a lower cash offer then a higher one with financing. By forgoing a somewhat lower cash offer, the owner is gambling that the property will a) sell and b) within a time period. Moreover, that it will sell for more then the cash offer minus the monthly carrying costs.
Hope this helps. Please contact directly if you would to discuss further.