Think about the task instead of the solution: you need to find the longest set of matching words which have letters in common. So start by doing two things: build a map of characters (there are only 26 possibilities 'A' to 'Z' inclusive) and count them for both your "check letters" and your individual words.
So your example "euclsfcysuls" maps to:
A 0
B 0
C 2
D 0
E 1
F 1
G 0
H 0
I 0
J 0
K 0
L 2
M 0
N 0
O 0
P 0
Q 0
R 0
S 3
T 0
U 2
V 0
W 0
X 0
Y 1
Z 0
That's trivial: a single pass though a word counting the letters. Write a method to do that and test it thoroughly.
Now it's an easier problem: for each word to check, find how many match by comparing the letter counts: if the "possible word" has a letter count greater than the same "check word" letter, it's not a match.
As you go through, keep a "longest so far" word, and when you find a possible match, compare that against the "longest so far" and update as needed.
At the end, you have the longest possible match.