> Is empty equal to not exist? 

No

a="" is an existing attribute node with string value empty.

If you want to copy attribute a if it exists and do nothing otherwise,
that's 

<xsl:copy-of select="@a"/>

If you only want to copy a if its value is non empty then that is

<xsl:copy-of select="@a[. != '']"/>

[. != ''] is, as you say, the same as [string(.) != '']
it is also the same as [string(.)] as in a boolean predicate the string
will be taken as true if it is non empty and false if it is empty.

David

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