"I was being neglectful by not feeding my cat on time"
I believe you meant to write the word "neglected."
The neglected flower wilted in its vase.
John neglected to turn off the lights when he left home yesterday.
The garden had been neglected for months, with weeds overtaking the flowers and shrubs.
She neglected to mention that she was married.
The neglected grapevine has lots of raisins.
The puppy, who had been neglected in forgotten for many years, eventually found a loving family.
The noble knight never neglected his duties.
The subject became woefully neglected as our food was allowed to become mediocre.
Yes, this sentence is grammatically correct, but you really don't need the second "that."
He's the main cause behind his insularity, he left his wife and neglected his close friends.
The word neglect is used to describe something or someone not being cared for in the proper way. An example of this word being used in a sentence would be, if you neglect the puppy, he will not grow up to be a happy, and healthy dog.