Learn English – “The earth was believed to be flat “

In newspaper headlines, editors tend to leave out as many words as possible for space-economical reasons. It also helps readers to read the headlines very quickly to rouse their interest in reading the rest of the article.

So "A man was robbed while he was sitting at home" becomes:

Man Robbed At Home

Some standard parts of sentences that are left out of headlines are:

• articles (a man -> man)
• auxiliary verbs (a man was slapped -> man slapped)
• copulative "be": (the new major is very happy -> New Major Very Happy)

There are many more, and it can be an interesting exercise to try and reconstruct a complete, correct sentence out of condensed headlines :)

Although a bit of ambiguity is not bad for a headline (it helps attract attention), in this case I do not see ambiguity.

If slapped was meant as an active verb, I would have expected the object to be mentioned - otherwise it makes no sense.

"A man slapped his neighbour" would become "Man Slapped Neighbour", not "Man Slapped Visiting Neighbours House".

For a headline like "Company Sued for Millions", I also see little confusion: if it is the company doing the suing, it is only news while the case is ongoing, so it would be "Company Sues For Millions"

The complement of believed in the usage in your question is either

--an infinitive-phrase with to at its head and the verb-to-be (to be, to have been) and its predicate complement:

He is believed to be responsible.

He is believed to have been responsible.

or

--the predicate complement with the verb-to-be omitted:

He is believed responsible.