I have heard from a few sources that the Prasad offered to Shivling should not be consumed by us. On searching stackexchange I found this post "Can devotees drink Abhishekam water" which talks about the water offered to the Shivling and there is no mention of prasad. So my question is are there any references in religious texts that clearly prohibit us from consuming the Prasad offered to Lord Shiva. And if it cannot be consumed then what should be done with that Prasad?
Actually whatever is offered to Shiva becomes 'Shiva-Naivedya' and 'Shiva-Nirmaalya', and is believed to be not to be taken back or consumed.
Devi asked this question to Shiva. Shiva replied : O Devi! Out of my five faces, the middle one is Shyamala Ishaana and the the one wpward is Kalaagni-rupa.nWhen I drank the halaahala after samudra- manthana, that poison stays always at my throat and that always provides burning sensation to my face. Whatever is offered on my face becomes not consumable by others,Because those things become brahmamaya, and so one who consumes these becomes fallen.
Whatever is offered to me should be just touched by head. That has to be offered to Vishnu by Vishnu-mantra and only then it can be consumed. My nirmalya is acceptable to Vishnu only and not to the ordinary entities like deva, asura ,gandharva, and manushya. (Omkarnath Rachanaavali, Sitaramdas Omkarnath,Vol 1, page 247-49)
For the Vaishnavas, Padma-Purana recommends that prasada of apShiva should not be consumed and nirmalya should thrown into well.(Ibid, page 249).
In another Purana, Shiva says that my naivedya and nirmalya are non-acceptable, but can be accepted after being touched by the Salagrama -Sila.(Ibid page 249)
According to Saktaananda-Tarangini, naivedya charanamrita of Shiva takes away all diseeases, sorrows and sins.
In Pranatoshini-Tantra, Shiva says that He has made the recommendation of not accepting His naivedya and nirmalya because these touching or consuming these gives moksha instantly. He who has not completed the birth ccles and cleansed sins should not get moksha. So I have made these recommendations. But the real fact is that even a chhandala gets moksha by consuming my naivedya(Ibid, page 251).
Omkarnathji concludes that Vaishnavas should accept these only after offering to Vishnu while the Shaivas can consume directly. But He prescribes general public not to consume these, unless the linga is Vaneswara."The owner of Shiva-Linga is Chandesh and so these offered items should not be consumed". (Ibid. page 251).