Here's the log:
https://www.dot.state.wy.us/files/live/sites/wydot/files/shared/Maintenance/Maintenance%20Section%20Reference%20Book/2017-MaintenanceSectionReferenceBook.pdfOn Page 95 of the PDF, we find the Johnson County map (yes I know we need to worry about Sheridan County we'll get there). This shows 193 as "ML1003B" and 87 as "ML346B". If we scroll down to the milepost logs (pg 98), we see that ML 1003B is labeled as US 87 & WY 193, and shows US 87 leaving I-90 at MP 98.290 and ending at WY 346 at MP 100.30; the route continues as WY 193. ML 346B is labeled as US 87, and branches off 87/193 at the previous junction. WY 346 is not mentioned until the Sheridan County page, page 141 (inset on pg 142 is clearer). There, ML 346B is labeled as WY 346, while ML 1003B is labeled as both 193/87 and standalone 193. 87 proper north of the Story area is ML 60B, and this continues to the north end of the washout. In the route log pages (starting at page 145), ML 60B is labeled US 14/87 BUS, I-90 BUS & US 87, and goes from MP 20.922 at I-90 Exit 20 to MP 40.850 where the description is "Roadway Ends @Slide Area". ML 1003B is only labeled WY 193, and goes from the county line to US 87. ML 346B here is labeled WY 346, and goes from the county line to the south end of the slide area.
After going through all that, the logs, especially in Johnson County, are kind of contradictory and confusing. My best attempt to sort out the situation is
1. Leave WY 193 as-is.
2. Truncate vanilla US 87 to the intersection with 193 and 346, since the southern spur is now signed as 346.
3. Add WY 346 to the southern washout spur.
4. Leave US87She as-is.
This, IMO, is the best combination of the signage on the ground, AASHTO's definition, and the WYDOT internal logs. As an aside, Wyoming's route inventory system is really quite bad, and needs to be overhauled.
I think the other stub is also in entoried as WY 344.
I remember that in the 2013 log, but the 2017 log has no record of it.