Due to the partner's hardships accessing empathy, he or she could consider incorporating cognitive empathy.
Intellectualisation, a defence mechanism, may allow the person to think logically about another person's experience and analytically show this understanding. Although not ideal, it can communicate a basic understanding of someone's experience.

Incorporating cognitive empathy

A person who possesses emotional intelligence regularly shows empathy, self-awareness and social awareness.
<ul>
<li>Empathy - the ability to understand another person's experience from their perspective.</li>
<li>Self-awareness requires a person to self-reflect, gain insight, and own up to selfish moments.</li>
<li>Social awareness is the ability to be emotionally attuned to others and really understanding a person.</li>
</ul>

The emotionally intelligent person

Feeling pity for someone is doable for an emotionally shortsighted partner. However, the partner needs to avoid the temptation to save and rescue. For example, "I'm sorry your dog died. I bought you a puppy so that you can feel better. You'll thank me later."
It is better to sympathise and encourage instead. "I am sorry your dog died. I feel bad for you. I hope you feel better tomorrow." It may sound hollows, but it provides support.

Encourage your partner to sympathize

Assist a partner in recognising when to offer cognitive empathy and sympathy. Remind them that when a person shows they are upset, the focus needs to remain on that person until they feel understood.
That means fully listening to the person and only providing an opinion or advice when they ask for it.

Know when to offer empathy and sympathy

People often find themselves involved with an emotionally unavailable person at some point. The person with deficits in emotional intelligence turn things around on others, avoid taking personal responsibility, and defends their position at all cost.
A person who cannot sustain closeness in a relationship often mistake control for closeness, inflicts guilt and makes unfair accusations to manage the other person.

The emotionally unavailable person

If small disagreements end in epic battles and your feelings are constantly disregarded, you may be involved with a person who lacks emotional intelligence.

The emotionally intelligent person

Similar ideas to The emotionally intelligent person

1.a. Tactical Empathy: Emotional Intelligence

The emotionally unavailable person

The three types of empathy