Obviously all the above posters are talking about the same song, folk-processed only in some details. JannaRae, your line "And then the old maid, who was wide awake..." suggests that the burglar had waited until he thought the lady slept. Still we are not told whether she had heard him and resolved to trap him, which I think would be the most logical explanation. Well, realism cannot be expected from such a song. Actually I don't think it is funny enough to be exempt from charges of invidiousness.

For scholarship's sake, here an ABC transcription from Wayne Erbsen, "Outlaw Ballads, Legends & Love":

X:1
T:The Old Maid's Last Hope
C:E. S. Thilp, 1887
K:G
L:1/16
M:2/4
Q:80
d2|B2 B A B B A A | B B A2 B3 A | G2 G2 A2 B2 | c4 z4 |
w:I'll tell you a sto-ry of a bur-g-lar man Who went to rob a house.
c c2 c A A A z | F F2 F D2 D D | d d d2 c2 A2 | B2G2 z2 |]
w:Went in the win-dow, crawled un-der the bed, Just as qui-et-ly as a mouse._

(ABC code can be entered at http://www.folkinfo.org/songs/abcconvert.php to obtain black dots or MIDI files.)