Maybe it's not "wszystkie". It's "wszysce".
No there isn't any Polish word with a form like "wszysce".
There are two different words:
"wszystko" - everything, which is a pronoun (it only inflects through 7 cases)
"wszyscy" - everyone, each and every person, which is an adjective (inflects through 7 cases + genders)
Now "wszyscy" is used with the personal masculine gender (nouns which represent people who are males, groups of people of both genders and groups of people of unknown gender), "wszystkie" is used with all other genders (all other nouns or groups of people which consist only of females)
My grammar book only gives one form for each case
Burn your grammar book :D
Declension of wszyscy:
M: wszyscy (animate masculine) / wszystkie (others)
D: wszystkich (all)
C: wszystkim (all)
B: wszystkich (animate masculine) / wszystkie (others)
N: wszystkimi (all)
Msc: wszystkich (all)
Declension of wszystko:
Note on using wszyscy/wszystkie:
When you use wszyscy/wszystkie you must either say what items do you have on your mind or it must be known from the previous conversation/text.
Also sometimes you can use it when you speak to a group of people (note that in such situation you must decide which gender you use, if you know there aren't any males use "wszystkie" otherwise use "wszyscy".) For example:
Idźcie wszyscy do domu! - (you all) go home!
Hope it helps.