In your case, use actual event names instead of ID numbers as unique values both in the URL and any database you are running in the back-end of your website.
Your rewrite rule probably (assuming your server is apache) has a line like this:
RewriteRule ^live/([0-9]+)/(.*)\.html$ processevent.php?ID=$1&Name=$2 [L]
Change that line to:
RewriteRule ^live/(.*)\.html$ processevent.php?Name=$1 [L]
Then again, you'll want to replace
.* with a stricter regex expression to ensure appropriate characters are in the URL. Maybe something like this will work better for you:
RewriteRule ^live/([A-Za-z0-9\-]+)\.html$ processevent.php?Name=$1 [L]
In your back-end script, access whatever database your script uses and use the event name to seek relevant data required to process the page. You may want to consider making the event name the primary key of the database table.