Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that Widdle is leaking urine.
I understand that she also has no tail.
Because Widdle was born without a tail she may be part Manx, or one of the other breeds that carry the genetics for short or no tails. Unfortunately tail-less cats are known for having abnormal nerve function at the end of their spinal cord (where the nerves that control the colon and urethra/bladder come off of the spinal cord) as the genetics that lead to short or absent tails can also affect spinal cord development.
If she is urine incontinent the concern is that bacteria can travel up an open urethra leading to secondary bladder and possible kidney infections. Those can become life threatening.
If she's dribbling urine on herself and isn't kept clean that can lead to urine scalding her skin and secondary burns and infections.
Is she able to pass stools normally?
Does she ever have any stiffness or difficulty with jumping or climbing stairs?
Given her dribbling and physical appearance I suspect that she does have some neurologic based trouble. Even if she is able to pass stools and seems to move normally she may still have altered nerve function. How severely she is affected will depend upon what sort of spinal cord defect she has.
If she's an outdoor kitten and she's able to pass stools and get around normally, and keep herself clean then she may be able to function for a while. But the concern will always be secondary infections.
I recommend that she see a veterinarian so they can try to determine how severely she is affected and what can be done for her.
Perhaps medication to help strengthen the muscles in her urethra could be an option for her if her only trouble is dribbling urine.
If your regular veterinarian is beyond your means financially now your other option is to contact your local shelter or humane society and see if they run a low cost clinic or know of one in your area.
If not here is a web-page that lists some that may be able to help:
Other sources of help can be found here: http://speakingforspot.com/?p=Financial%20Assistance%20for%20Veterinary%20Care
Please let me know if you have any further questions.