The connection is simple.
Parsing encounters erroneous incompatible quotes, which results in the inability to check the rest of the text where the footnote text is located, hence the message about the unidentified fragments.
Incompatible quotes are dangerous and I don't understand where they would come from in Sigil, which takes great care to ensure that the code is well-formed. You simply have to be careful when editing your code to avoid such situations.
Here is another example of a file that, when you run the "Mend" option, causes the contents to be cleared.
Code:
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN"
"http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title>Test</title>
</head>
<body>
<div class='badclass">
<h1>Chapter</h1>
<p class="first">Blah</p>
<p>Blah<a id="fn1" href="#fntext">[1]</a></p>
<div class="footnotes">
<div class="footnote">
<p><a id="fntext" href="#fn1">[1]</a> Footnote 1</p>
</div>
</div>
</div>
</body>
</html>