Assuming you meant a 128-bit hash with all bits set to '1' (i.e., '0xffffffffffffffffffffffffffffffff'), it would still be extremely difficult, if not practically impossible, to find a string that hashes to this specific value. The MD5 algorithm is designed to produce seemingly random output for small changes in input, and there are no known methods to easily reverse-engineer an MD5 hash.
That being said, MD5 is no longer considered cryptographically secure due to vulnerabilities discovered over the years, such as hash collisions. But finding a specific hash, like the one you mentioned, would still require a brute-force attack or an advanced cryptanalytic method, neither of which is guaranteed to succeed.
My statement is one of statistically-informed confidence. A physicist's proof, not a mathematician's. As I said, proving it is where the challenge lies.
The linked answer on SE basically says statistically there's a near-100% chance that there's a string where md5(string) is 0xfffffff... but there's no concrete proof.
I tried seeing if there were any references in log files or forum questions to that, but the bad news is that your specific hash is also what one would get from an "invalid" hash, same as asking about the magic string "00000000000000000000000000000000"
That being said, MD5 is no longer considered cryptographically secure due to vulnerabilities discovered over the years, such as hash collisions. But finding a specific hash, like the one you mentioned, would still require a brute-force attack or an advanced cryptanalytic method, neither of which is guaranteed to succeed.