(First, let's get a technical grammatical issue out of the way. The verb form employed in your a-type sentences is not a past participle but a simple past. With most verbs the two forms are identical, but they have to be distinguished because with some (not all) irregular verbs they are different: be for instance has the simple past forms was and were and the past participle been.)
What is tripping you up here is the peculiar semantics of worry. In your 'base' sentence
He worried that supplies were running low.
worry looks like a transitive verb with the that clause as its direct object, but this is not the case. This sentence employs a secondary sense of worry as an middle-voice verb combined with a that complement, borrowed from the transitive version of worry, which expresses the cause.
What is going on with the that complement may be illustrated with some similar transitive verbs which signify causing strong emotion:
X frightens me passivized as I am frightened by X.
X angers me → I am angered by X.
X disgusts me → I am disgusted by X.
X delights me → I am delighted by X.
X worries me → I am worried by X.
But English does not like using that clauses as objects of prepositions.
∗ I am frightened by that he got the promotion.
Consequently, with all of these verbs the passive version takes a different form when X is a that clause. There are several solutions. Anger, for instance, prefers to recast angered as the frank adjective angry:
That he got the promotion angers me → I am angry that he got the promotion.
The that clause may be recast as a gerund clause:
That he got the promotion frightens me → I am frightened by his getting the promotion.
But gerund clauses can't be created from that clauses with a modal head verb, so most verbs also license the that clause with the preposition deleted:
I am disgusted that he may get the promotion.
I am delighted that he may get the promotion.
I am worried that he may get the promotion.
An odd thing happens, however, with that last sentence. The ‘base’ modern sense of the verb worry is transitive: to ‘cause someone to feel anxiety’. Fairly recently, by linguistic standards, it developed secondary senses: a noun meaning ‘anxiety’, and an intransitive verb meaning ‘to feel anxiety’. The intransitive verb developed out of the transitive verb by way of a reflexive worry oneself, and it is in effect a ‘middle-voice’—the same sort of thing we see with the verb cook:
ACTIVE VOICE: I am cooking eggs.
PASSIVE VOICE: The eggs are being cooked.
MIDDLE VOICE: The eggs are cooking.
Usually this middle-voice worry expresses its cause with a preposition phrase: I worry about his getting the promotion or occasionally over his getting the promotion. But since about 1960 there has been a growing tendency to borrow the active version's that complement:
I worry that he may get the promotion.
That is what you have in your 2a. But note: this is not a transitive usage. I worry does not take a direct object, so it cannot be passivized. The passive-voice sense is already ‘built in’ to the middle-voice expression: I worry means, at least syntactically, the same thing as I am worried, just as the eggs are cooking means the same thing as the eggs are being cooked.
And that is why you cannot say "it was worried*.
