I Googled for "at the home of Madge Malone" and found this at another forum:

It was on a Tuesday evening at the home of Madge Malone.
There was quite a celebration for her parents weren't home.
There were songs and witty stories, and a bottle on the shelf
When up sprang Dan McGrew and said, "Here's a song I wrote meself!"
"Sing it, Dan!" "Righto, I will."

She was just a sailor's sweetheart
And she loved her sailor lad,
But he left her broke in Hartford;
He was all she ever had.

But she still believes in sailors,
And she's true to the red white and blue,
And tho' she got sore,
When he broke her jaw,
Oh, she loves her sailor boy absolutely.

The person who posted it said he learned the words from a piano roll. Note the subtle changes. The text has been expurgated. I guess the publishers wanted to avoid the scene of kids gathered around the piano asking, "Mom, why was she barred from the Navy Yard?" And "positively" has been changed to "absolutely," which reinforces my interpretation of the original.

And it just dawned on me: "broke in Hartford" is a pun on "broken-hearted." That joke is relatively clean, so they left it in.

Here's a view of the sheet music cover.

I also learned that (coincidentally, I assume) MADGE MALONE is the name of a tune by Turlough O'Carolan.