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.
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