Does a Buddha or arahant like food and is mindful of that liking at all times or does liking just no longer arise? Does the Buddha like or dislike at the heart level and yet sees the heart objectively?
Related to this question: What is the basis?
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Feelings (vedana) are of one of these types: pleasant, painful or neutral.
Arahants will experience all these types of feelings.
However, the three poisons of lust or greed (lobha), aversion (dosa) and delusion (moha) will not arise in arahants. Craving (tanha) and clinging (upadana) will also not arise in arahants.
Liking a feeling is basically lust or greed (lobha). So, this does not arise in arahants. They would only endure the pleasant, painful or neutral feeling mindfully.
This falls under the heading of Guarding the Senses; one of several practices in the creation of self-discipline: Jagarianuyoga
A previous act of identification with the activities that started the process [intent to create personal experience coupled to deeds of body, speech and mind] puts a sort of 'mark of ownership' on the consequences and it is identifying (claiming, recognizing) these markers that results in the experience known as "My sight", or "I am seeing."
The experience of sensation — that is, the subjective reaction to or evaluation of the unpleasant or pleasant (physical, verbal or mental) — changes in accodance with whether or not the individual is oriented to gain in the experience of worldly pleasures or to attaining an end to kamma. For example the experience of pleasant sensation arising from kamma to be experienced as worldly pleasure can be changed to the perception of the unpleasant implications of that situation for one seeking to end kamma. Thus the pleasant can be experienced as pleasant or unpleasant, the unpleasant can be experienced as unpleasant or pleasant, or both can be experienced indifferently.
Arising from this experience comes liking or disliking depending on the sensation and whether or not one's original intent was to create worldly experience or to escape the world.
Both liking and disliking, are, in the Pali, forms of wanting and lead to action that repeats the cycle and results in an outcome determined by kamma.
For this reason, the beggar trains himself to be wary of sights, sounds, scents, flavors, touches, and thoughts.
Being aware of the danger, he guards "The Doors of the Senses" and when an object of sense comes into the range of an organ of sense, he neither dwells on its general appearance nor it's details. — He is aware of it, but does not 'think about' it or dwell on the sensation associated with it or take delight in it or react to it's influence or say to himself 'sensing, sensing, sensing'.