Do old passports have to be submitted?
Yes — the document says old passports must be submitted with the application form.
In detail
This is the document's second requirement: “Old passports must be submitted with the application form.” It appears identically under every visa category, so it applies whether you are applying for tourist, medical or business.
Putting the expired passport away once the new one arrives is a normal habit, which is why many people arrive without it. Find it in advance.
What to do if an old passport is lost or otherwise unavailable is not covered by the official document. We are not going to invent a rule for it — asking at the application centre is the only reliable route in that situation.