Format preserving numbers within an offset range?

Is it possible to encrypt a sequence of numbers with FPE in a range 10 000 to n where the possible encrypted values are offset and can only fall within the range 10 000 to n?

Easily; here's a straight-forward 3 step process to encrypt a value $x \in [10000, n]$:

• Subtract 10000 from n

• Encrypt it using an FPE method that handles a range $[0, n-10000]$. This may involve selecting an appropriate base, and possibly reencrypting the ciphertext if it falls outside the range

• Add 10000 to the result

The corresponding decryption process should be obvious...

And, the standard way to handle plaintexts/ciphertexts in a range $[0, x]$ with a base $b^e > x$ is:

• Express the plaintext as $e$ base-$b$ digits (using a base conversion routine)

• Encrypt the plaintext using the key

• If the result happens to be $> x$, then reencrypt that result with the same key (and repeat until the result is in range)

• Convert that result into the ciphertext (using another base conversion routine)

This takes variable time, however it doesn't leak any information (as the attacker cannot deduce anything from an intermediate result being out of range). And, it will always halt (as FPE encryption is a bijection, the result of multiple encryptions will be a cycle, and so as long as you start with a value within the range, you'll end up with a value within the range)