I was wondering if death`s shadow would actually get bonuses if the player who controls it has a negative life.

No, because there is no +X/+X effect on Death's Shadow so once you hit negative life he just stays a 13/13

Lol....actually looking at that again I change my statement to I don't know....because technically according to math a double negative IS a positive....so I want to say yes but I don't have the proof to do so with the exception of actual math.

Ok back....after doing some research I found this:

107.1b Most of the time, the _Magic_ game uses only positive numbers and zero. You can't choose a negative number, deal negative damage, gain negative life, and so on. However, it's possible for a game value, such as a creature's power, to be less than zero. If a calculation or comparison that would determine the result of an effect needs to use a negative value, it does so. If such a calculation yields a negative number, zero is used instead, life total to a specific value, sets a creature's power or toughness to a specific value, or otherwise modifies a creature's power or toughness.

So basically Death's Shadow would stay a 13/13

Uhm....how so? The rule you just mentioned seem to say otherwise. Lets split it into parts:

"If a calculation or comparison that would determine the result of an effect needs to use a negative value, it does so".
Therefore we use the negative life to calculate and...the calculation results in a positive number.

"If such a calculation yields a negative number, zero is used instead, life total to a specific value, sets a creature's power or toughness to a specific value, or otherwise modifies a creature's power or toughness"
Our result is positive (+4/+4 for example), therefore it wont use zero instead.

...or did I misunderstand something?

PS: I know you are right, but its just fun to argue in favor of this

how the hell would a player have negative life and still be in the game lol

There are plenty of ways to play at negative life.....Lich's Tomb, Platinum Angel, your opponent owning an Abyssal Persecutor, etc.

I had precisely those 3 in mind

indeed - really confusing situation... unless magic defies the laws of basic math it seems to me the creature would be 13/13 lol