Bali-mardana: I believe I've heard you said in other lectures that a person who takes prasädam, even a plant or a..., any kind of living entity who takes prasädam or hears the name, that it will come back at least to human form of life. Is that correct?
Prabhupäda: No, if he's devotee, then he'll come. But this taking of prasädam, or hearing Hare Krishna mantra is advancement for becoming a devotee. But if he takes prasädam not as ordinary prasädam, foodstuff, he believes that "This is remnants of foodstuffs given to God," if he understands this philosophy, then guaranteed. If he takes the prasädam as ordinary food, "All right, these people are distributing, prasä... Let me take it. It is very tasteful," that will give him chance to accept prasädam next, next, next... In this way, one day he'll come to the point that "This prasädam is not ordinary foodstuff." Then he'll... There is guarantee. Because only the devotee can appreciate that "This prasädam is not ordinary foodstuff. It is Krishna's remnant of..." Therefore, he understands Krishna. That is said in the Bhagavad-gitä, janma-karma ca me divyam yo jänäti tattvatah [Bg. 4.9]. In truth, when he understands, then his life is guaranteed. Why guaranteed? He goes back to home next life. Tyaktvä deham punar janma naiti [Bg. 4.9]. If you simply can understand what is Krishna and what is your relationship with Krishna, that is sufficient to take you back to home, back to Godhead. That is sufficient. It is so nice.
Antya 1.32

āra dina keha tāra dekhā nā pāilā

siddha-deha pāñā kukkura vaikuṇṭhete gelā

SYNONYMS

āra dina — the next day; keha — all of them; tāra — of the dog; dekhā nā pāilā — did not get sight; siddha-deha pāñā — obtaining a spiritual body; kukkura — the dog; vaikuṇṭhete gelā — went to the spiritual kingdom, Vaikuṇṭha.

TRANSLATION

The next day, no one saw that dog, for it had obtained its spiritual body and departed for Vaikuṇṭha, the spiritual kingdom.

PURPORT

This is the result of sādhu-sańga — consequent association with Śrī Caitanya Mahāprabhu and promotion back home, back to Godhead. This result is possible even for a dog, by the mercy of the Vaiṣṇava. Therefore, everyone in the human form of life should be induced to associate with devotees. By rendering a little service, even by eating prasādam, what to speak of chanting and dancing, everyone can be promoted to Vaikuṇṭhaloka. It is therefore requested that all our devotees in the ISKCON community become pure Vaiṣṇavas, so that by their mercy all the people of the world will be transferred to Vaikuṇṭhaloka, even without their knowledge. Everyone should be given a chance to take prasādam and thus be induced to chant the holy names Hare Kṛṣṇa and also dance in ecstasy. By these three processes, although performed without knowledge or education, even an animal went back to Godhead.

I've heard that eating Prasadam clears away all your past sinful activities. But, I wouldn't think it would directly prevent future sinfulness, which would indeed keep you human, or worse! I would say that on going devotional service (chanting, reading scripture, prayer, etc.) would be the best way to keep a future where human life would be a worst case scenario!

Having said all that, I'm hoping to work out a way that I can offer a simple prasadam to Lord Krishna, that I could then share with my pets! After all, kitties and dogs have karma, too!