If I delete a product should I remove its link from the *sitemap.xml* also? Is there any penalty from Google for leaving a lot of dead links in my sitemap? What is the most common practice and why?

It seems to me illogical to offer somebody non-existent content. This way I could fake 1000 or more links, just by creating wrong URLs with nice names. Or am I wrong?

Does it matter if sitemap.xml is up to date or not? I can update it every day via cron, so that's not a problem.