Can a result of (any) hash algorithm contain the hash result itself?

Suppose you have a file of 240 lines. Any lines, any content. You then calculate the hash of that file, let's say MD5, and the result is something in the following structure:

    f8dbe310c1f61066d766071b07503ce8

Now, you take this hexadecimal digest, and add it to the file as line 241.

Rehashing the file (with additional hash line) will result with a new hash value obiously.

My questoin is whether it is even theoretically possible for a hash value to contain itself, meaning, can there be a file, with some content that its hashed value is identical to a string already presented in the file (e.g. line 241 in this example)