Genealogy research online is mostly about ancestors rather than descendants because records available are fairly limited after 1930. However, records about ancestors often have clues to descendants and relatives. There are severe limitations on availability of public records of people to those who do not have a close blood relationship to the person whose records are sought. Also, public records online with more than minor information and more recent than the 1940's are few and far between.
That said, since it isn't clear that you have searched various records that are available online, here are some of them. Perhaps they have some clues to the relatives of your great-aunt. The names are written exactly as indexed on ancestry.com:
The Social Security Death Index (SSDI) shows Mary Pugzlis, living in Cicero (Cook County), Illinois, born on March 15, 1892, died January, 1974.
The SSDI shows Paul Pugzlis, living in Cicero (Cook County), Illinois, born on April 27, 1885, died November, 1974.
A WWII military draft record of April 27, 1942 for:
Paul Pugzlis, born April 27, 1884, living at 1419 49th Ave., Cicero (Cook County) Illinois, born in Kalnaliskei, Rokiskis, Lithuania. Person most likely to know whereabouts: Mary Pugzlis, wife. Working at Hotpoint General Electric Co., in Cicero.
The 1930 U.S. Census for Cook County, Cicero, Ill., 1419 49th Avenue shows:
Paul Pugzlis, age 43 (born around 1887 in Lithuania), arrived in the U.S. in 1911, working in a factory as a laborer, had filed papers for U.S. citizenship
Mary Pugzlis, age 36 (born around 1894 in Lithuania), arrived in the U.S. in 1913
Stefsuie Norvel, age 15 (born around 1915 in Illinois as were the other children), (notation may that she is the step-daughter of Paul, and therefore, daughter of Mary by a previous marriage) (given name is a mistranscription of Stefanie)
Elizabeth Pugzlis, age 8 (born around 1922)
John Pugzlis, age 9 (born around 1921)
Julia Pugzlis, age 4 years and 5 months (born Dec., 1926)
Paul and Mary were married around 1919.
The 1920 U.S. Census for Cicero (Cook County) Illinois, 1517 49th Court shows:
Paul P Pugzels, age 35 (born around 1885 in Russia, mother tongue Lithuanian), arrived in the U.S. in 1911, working as a trucker, applied for U.S. citizenship
Mary A Pugzels, age 26 (born around 1894 in Russia), arrived in the U.S. in 1913, working as a "machine hand" in a tobacco factory, applied for U.S. citizenship
Stephina Pugzels, age 4 years and 10 months (born around March, 1916)
By the way, since the ending "-aite" is reserved for the unmarried daughters of man whose surname ends in "-as" or "-a", perhaps you mean to say that Marijona's surname or family name was Meis^tininkatie and her father's surname or family name was Meis^tininkas.