code:
 
<xsl:function name="fun:runerror">
    <xsl:copy-of select="1 div 0"/>
</xsl:function>
<xsl:variable name="x" select="fun:runerror()"/>
<!--или <xsl:variable name="x" select="1 div 0"/> -->

code:
 
<xsl:function name="fun:runerror">
    <xsl:copy-of select="1 div 0"/>
</xsl:function>
<xsl:variable name="x" select="fun:runerror()"/>
<!--или <xsl:variable name="x" select="1 div 0"/> -->
<xsl:value-of select="$x"/>

В ответ на:

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То есть получается, что exception хранится в переменной и если мы не сделаем что-нибудь из
<xsl:value-of select="$x"/>, <xsl:copy-of select="$x"/> или <xsl:message select="$x"/>, то преобразование благополучно закончится.

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DevChannel | Overview of an XSLT stylesheet:

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Lazy evaluation. With a functional language such as XSLT, the only result of a variable declaration is that the variable now exists; no side effects are possible or allowed. This allows the XSLT processor to optimize stylesheet execution by declaring the variable only when - and if - necessary. This feature is called lazy evaluation, but not all XSLT processors behave that way; one of the "lazy" processors is Saxon.

Lazy evaluation means that if, for example, your xsl:variable declaration contains a debugging output (xsl:message) or a document creation instruction (xsl:result-document), neither will ever get control if its parent variable is not used. And the variable may remain unused simply because none of the templates that reference it are triggered by the current source document.

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В ответ на:

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Вопрос: как можно остановить преобразование внутри функции?

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XSLT2 - 2.9 Error Handling:

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In cases where an implementation is able to produce the final result trees without evaluating a particular construct, the implementation is never required to evaluate that construct solely in order to determine whether doing so causes a dynamic error. For example, if a variable is declared but never referenced, an implementation may choose whether or not to evaluate the variable declaration, which means that if evaluating the variable declaration causes a dynamic error, some implementations will signal this error and others will not.

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В ответ на:

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Может я не в тему, но погуглив "xslt lazy evaluation", нашел в частности вот такое:

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В ответ на:

---

А как ты себе представляешь остановку преобразования?

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code:

<xsl:template match="XXX">
....
    <xsl:variable name="x" select="f:getX($y)"/>
....
</xsl:template>
<xsl:function name="f:getX">
   <xsl:param name="y"/>
   <xsl:variabble name="tmp" select="f:checkPar($y)"/>
   .....
</xsl:function>
<xsl:function name="f:checkPar">
   <xsl:param name="y"/>
   <xsl:variabble name="tmp" select="if (not($y)) f:runError()"/>
</xsl:function>
<xsl:function name="f:runError">
  <xsl:message select="error(collection(),'Err_Info')"/>
</xsl:function>