is there a charset that can be used to circumvent this issue?

You mean "character encoding", not "character set". The question is:

Is there a character encoding that can represent the Unicode character set?

All UTF-* encodings can handle all Unicode characters.

There's obviously something missing to the question since you started off with such a character encoding (UTF-16be).

Also worth mentioning are the UCS-2* encodings. UCS-2le and UCS-2be are the fixed-width subsets of UTF-16le and UTF-16le. They can handle a big chunk of Unicode (U+0000..U+FFFF).

Windows uses UCS-2le internally and uses this for its Wide interface. UTF-8 is the charset of choice elsewhere.

In fact, unix terminals tend to expect UTF-8 these days. It kinda surprised me when you asked for iso-8859-1.