I was about to say it is "sweetened pearl onion pickles", then after reading your context, it become clear that she struggled with raw stuff, washing them, peeling them in preparation of, probably, making らっきょう漬け pickles for her husband.
らっきょう漬け is a traditional, and common condiment of almost every Japanese households, and made of one single ingredient of pearl onion with a lot of sugar and some vinegar thrown in.
allion (green onion) root, but certainly a type of onion root vegetables.

Scroll this site to half way through.
http://blogs.yahoo.co.jp/jang_shogun/folder/881579.html

Also:
http://www.answers.com/topic/pearl-onion

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Note added at 39 mins (2006-08-12 01:42:55 GMT)
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Woops, few word are missing. Read the last part as ***I do not think this is a sc** allion (green onion) root, but certainly a type of onion root vegetables like garlic.


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Note added at 57 mins (2006-08-12 02:00:35 GMT)
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After I see picture on this site, I am not sure they are same as shapes are quite different. http://www.melissas.com/catalog/index.cfm?info=yes&product_I...
Moreover, this seems a produce particular of Japanese soil (origin still unknown) so I correct my answe to:
Japanese variety Pearl Onions