INSERT INTO table VALUES('1','<p><em>The lazy fox jumps again</em></p>bunch of other html<p><em>Is the lazy fox crazy?</em></p>')
INSERT INTO table VALUES('2','<p><em>The lazy fox jumps again</em></p>bunch of other html<p><em>Is the lazy fox crazy?</em></p>')
INSERT INTO table VALUES('3','<p><em>The lazy fox jumps again</em></p>bunch of other html<p><em>Is the lazy fox crazy?</em></p>')

INSERT INTO table VALUES('1','The lazy fox jumps againbunch of other html<p><em>Is the lazy fox crazy?</em></p>')
INSERT INTO table VALUES('2','The lazy fox jumps againbunch of other html<p><em>Is the lazy fox crazy?</em></p>')
INSERT INTO table VALUES('3','The lazy fox jumps againbunch of other html<p><em>Is the lazy fox crazy?</em></p>')

sed "1,/INSERT INTO/s/<p><em>//g"

sed -e '/INSERT INTO/s/<p><em>//' -e '/INSERT INTO/s/</em></p>//'

perl -pe 's:<p><em>(.*?)</em></p>:$1:' infile

INSERT INTO table VALUES('1','The lazy fox jumps againbunch of other html<p><em>Is the lazy fox crazy?</em></p>')
INSERT INTO table VALUES('2','The lazy fox jumps againbunch of other html<p><em>Is the lazy fox crazy?</em></p>')
INSERT INTO table VALUES('3','The lazy fox jumps againbunch of other html<p><em>Is the lazy fox crazy?</em></p>')