My understanding of the original question is: There is a Writer file and within the text there is FRAME inserted and there is also text within this frame.
I am bit surprised that MSO allows a selection of a text AFTER double-clicking a word because double-clicking a word is in MSO also the selection for an entire word. Thus, when you pull the cursor, the selected word should move. Therefore, the ability to select a word by double-clicking and drag down to select the entire text with the mouse looks to me like a MSO bug, which appears to be appreciate by you.
I made a test in LibO 4.0.4:
double clicking selects the word
triple clicking selects the first sentence
quadrupole clicking selects the paragraph
Thereafter you need to do ctrl+a or insert the cursor before the first character you want to select and pull down until the end of what you want to select.
I attached my test file here. Make sure you first download the file. Opening the file only keeps the file in save mode = read only.
I can do this at my computer.. I double clicked the first word, didn't relase click and move it right or left, without any problem...