You didn't specify the XSLT version you're using, so I'm assuming XSLT1. Also,
your sample output is missing the root element, which means it's not well-formed XML, so I added one.
Here's one option:
<?xml version="1.0" encoding="utf-8"?>
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:xs="http://www.w3.org/2001/XMLSchema"
exclude-result-prefixes="xs">
<xsl:output method="xml" indent="yes"/>
<!-- Match the root node of this document -->
<xsl:template match="/">
<!-- Create the <root> element so that the document has a root element. -->
<root>
<xsl:apply-templates/>
</root>
</xsl:template>
<!-- Match the <match> element. -->
<xsl:template match="match">
<xsl:apply-templates select="test/string" mode="match"/>
</xsl:template>
<xsl:template match="string" mode="match">
<!--
Apply the closest ancestor <match> element of the current <string> element.
-->
<xsl:apply-templates select="ancestor::match[1]" mode="match">
<!--
Pass the current string element as a parameter to the matched template.
-->
<xsl:with-param name="string" select="."/>
</xsl:apply-templates>
</xsl:template>
<xsl:template match="match" mode="match">
<!--
If you're using XSLT2, you can use a tunnel parameter, in which case you
don't have to specify the parameter here.
-->
<xsl:param name="string"/>
<!-- Copy this <match> element into the output as is. -->
<xsl:copy>
<!-- Apply the attributes of this element with the default mode. -->
<xsl:apply-templates select="@*"/>
<!--
Apply the child nodes (element or text) with the "match" mode. Pass the
<string> element we passed as a parameter earlier on to the applied
templates.
-->
<xsl:apply-templates select="node()" mode="match">
<xsl:with-param name="string" select="$string"/>
</xsl:apply-templates>
</xsl:copy>
</xsl:template>
<xsl:template match="test" mode="match">
<!--
Remember, this parameter points to <string>Foo</string>,
<string>Bar</string>, or <string>Baz</string>.
-->
<xsl:param name="string"/>
<!-- Copy this element as is. -->
<xsl:copy>
<!-- Copy its attributes as is, too. -->
<xsl:apply-templates select="@*"/>
<!--
Don't copy any of the child elements as is: rather, create a copy of the
<string> element we passed as a parameter here.
-->
<xsl:copy-of select="$string"/>
</xsl:copy>
</xsl:template>
<!--
For every other attribute, element or text node that is applied with the
"match" mode, defer to the default mode. In this case, that means deferring
to the identity transform template (see below).
-->
<xsl:template match="@* | node()" mode="match">
<xsl:apply-templates select="."/>
</xsl:template>
<!--
Identity transform: every attribute or element matched by this template into
the output as is.
-->
<xsl:template match="@* | node()">
<xsl:copy>
<xsl:apply-templates select="@* | node()"/>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>
Output:
<root>
<match target="font">
<test name="family" compare="eq">
<string>Foo</string>
</test>
<edit name="embeddedbitmap" mode="assign">
<bool>false</bool>
</edit>
</match>
<match target="font">
<test name="family" compare="eq">
<string>Bar</string>
</test>
<edit name="embeddedbitmap" mode="assign">
<bool>false</bool>
</edit>
</match>
<match target="font">
<test name="family" compare="eq">
<string>Baz</string>
</test>
<edit name="embeddedbitmap" mode="assign">
<bool>false</bool>
</edit>
</match>
</root>