Modal auxiliaries are always finite and followed by passive present (be verb+ed participle) or past (have been verb+ed participle) infinitive. Passive infinitive states that the subject of the sentence is not the agent of the action denoted by the infinitive. Present infinitive refers to present or future, whereas past infinitive refers to past when used with modal auxiliary verbs.

“It must be done that way.”(present passive infinitive)
“It must have been done that way.”(past passive infinitive)

Passive voice with the presence of modal verbs is rare in general conversation, but occurs widely in academic writing.

According to corpus findings stated in Biber (1999, 499), will, would and shall are rare with passive voice as they frequently express volition or prediction of the agent of the main verb. On the other hand, can and could are very common in passive structures where they denote logical possibility and occur in short agentless passives or in passives with a nominalized process given in the by-phrase. In academic prose, must and should are commonly used, mainly because of their ability to express obligation.

Research
1.Central modals
a)Present / future reference

CAN
In Italy, Australia is considered an attractive alternative where jobs can be found, and it has a large Gypsy population.
The other gate is built like a Dutch door, so the top and bottom halves can be opened separately.
The mirror, its frame carved with cherubs, can be tilted to provide an overhead view of the pen, as a cooking-school mirror provides the pupils with an overhead view of the stove. Dr Lecter thinks he can be swept through with the herd, as long as the herd accepts him. But Memory Charms can be broken by a powerful wizard, as I proved when I questioned her. The full list comprises some four hundred and thirty-seven items, I believe, and can be viewed in Mr. Filch's office, if anybody would like to check it. The Imperius Curse can be fought, and I'll be teaching you how, but it takes real strength of character, and not everyone's got it. "I don't reckon it can be done," said Ron's voice flatly from the other side of the table. No, I haven't actually seen him, but I think I can be trusted to know my own superior's handwriting. Pigs are harder to get hold of than men and big ones are stronger than a man and they cannot be intimidated with a gun.

COULD
Now, should the universe contract, should time reverse and teacups come together, a place could be made for Mischa in the world. "I'm coming over there. I could be deputized and go with the reactive squad." He could be blamed. Even if they were good and hungry, sixteen pigs could not be expected to consume Dr Lecter in his entirety at one seating. They could not be tightened now. Frank was nearing his seventy-seventh birthday now, very deaf, his bad leg stiffer than ever, but could be seen pottering around the flower beds in fine weather, even though the weeds were starting to creep up on him, try as he might to suppress them. "It could be done without Harry Potter, My Lord." Voices could be heard from inside the blocked fireplace. Lynch, however, hit the ground with a dull thud that could be heard throughout the stadium. The buzz of chatter filling the Hall ceased almost at once, so that only the howling wind and pounding rain could be heard. And in no time at all, hundreds upon hundreds of pairs of feet could be heard passing the tent, their owners talking excitedly, laughing, joking... "Come off it," said Harry, looking around to check that they couldn't be overheard, but the grounds were quite deserted.

MAY
It may be defined for laymen as the act of posturing as a wise and caring patron to further a private agenda. Human destiny may be deciphered by the planetary rays, which intermingle...