HTML corrector doesn't close quotation marks in teaser
Doesn't look like it's a problem on your side. You can try the following:

drush php-eval '$text = "&lt;ul&gt;&lt;a href=\"http://goo"; print $text . "\n"; print _filter_htmlcorrector($text) . "\n";'


And for me the results are:

&lt;ul&gt;&lt;a href="http://goo
&lt;ul&gt;&lt;a href="http://goo&lt;/ul&gt;


(The second line is the output of _filter_htmlcorrector().)

It would be worth seeing if there's an issue for this already, and if not creating one. I find the built-in HTML corrector too limiting anyway (it always strips styles for example IIRC), and use htmLawed. With that you get:

drush php-eval '$text = "&lt;ul&gt;&lt;a href=\"http://goo"; print $text . "\n"; print htmLawed_filter('process', 0, -1, $text) . "\n";'


Results:

&lt;ul&gt;&lt;a href="http://goo
&lt;ul&gt; &lt;/ul&gt;


(Again, second line is the cleaned output - it's simply stripped the incomplete tag.)