“They came in through the basement and the lady that occupies the space downstairs, said they can wiggle the window and come in very easily.”
I felt for the poor woman, having burglars come through her: that experience must have been physically trying and reminiscent of reverse childbirth. The comma is incorrectly placed, as you should never separate the subject from its verb unless it is a qualifying phrase that follows the subject. A more specific version of this sentence should read:
“The burglars came in through the basement window. The lady, who occupies the space downstairs, said that the window can be wiggled open easily.”
Firstly, I thought it better to cut the sentence into two for clarity. The first is the event in question; the second sentence qualifies the first. Next, I specified who the ‘they’ were, as it is always better to specify the subject rather than having an orphaned pronoun. As the impetus of the initial sentence was to include a comma, I created am appositive phrase to modify the subject, the “lady.” The commas are not necessary but I am a fan of commas to help provide a nicer rhythm to a sentence, and to help break out concepts. I next added “that” to turn the object of the second sentence into a stronger clause. Lastly, I condensed the two ideas, of the window being wiggled and of the burglars coming in easily, together, for increased clarity.
Voila! The recipe for a better sentence.