If you wanted to remove an element, and all its descendants, you would do this...
<xsl:template match="child" />
However, if you simply wanted to remove the element, but keep its descendants, you would do this...
<xsl:template match="child">
<xsl:apply-templates />
</xsl:template>
Where <xsl:apply-templates /> is short for <xsl:apply-templates select="node()" />
Try this XSLT
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" version="1.0">
<xsl:output method="xml" indent="yes" />
<xsl:strip-space elements="*" />
<xsl:template match="child|value">
<xsl:apply-templates />
</xsl:template>
<xsl:template match="@*|node()">
<xsl:copy>
<xsl:apply-templates select="@*|node()"/>
</xsl:copy>
</xsl:template>
</xsl:stylesheet>