I know this happened with Cyrillic in Russia in the time of Peter the Great, for example.
Another example is modern Gujarati script, which started off as a much simplified informal commercial handwriting variant of early Devanagari. The commercial script left out free and bound characters for short vowels, only marking long vowels, and used full letters when vowelless instead of conjunct forms of letters; as well, the more complex letter shapes of Devanagari were simplified by incorporating the headstroke into letters in different ways, raising the location where the crossbar joined the stem to the top, and simplifying some more complex stroke sequences at the top of letters. You can still find these in more informal adult handwriting and they were kept for the most part in Kaithi, which also derived from the early informal handwriting.
Modern Gujarati (that is to say modern Gujarati typefaces and careful handwriting) took the older handwriting and made some changes that brought it back closer to Devanagari. The join between cross-strokes and the stem was brought back down to mid-stem, letters and vowel marks for both long and short vowels were reintroduced using Devanagari as a model, and conjuncts were reintroduced, also on the model of Devanagari.
Another example is the way the indigenous old Philippine script (Baybayin, Basahán or Alibata are the three main names) was adapted typographically in the early 1600s, giving the strokes of the letters a nibbed pen-like modulation alien to the original script, which was incised into bamboo or leaves; however, this modulation was what seemed appropriate for printing types to the Spanish who printed several books using the modified print version of the script.
I even have the impression that the modulated appearance of the standard printing version of modern Javanese script may also have been inspired by European script. The ductus of Balinese script is in fact identical to the way the letters of Javanese script were written, incised into lontar (palm leaf strips) before the 19th century, and even at the time, written with ink on paper. They are really the same script apart from the superficial change in appearance of Javanese script in the 19th century.
And in Europe, the older uncial-based form of Latin script used for Irish was abandoned in the mid 1900s for the Italianate humanist-based version we are used to. The same happened to the traditional North European blackletter, which was gradually replaced in Scandinavia, the Baltic and Bohemia in the 19th Century, leaving Germany as the last holdout, where it was abandoned in the late 1940s for the Italianate "Antiqua" that is now universal.
As for scripts designed for writing on hard surfaces like wood being modified to more cursive forms, that is almost exactly what happened to Lampung script in South Sumatra. It started off indistinguishable from the Rejang-Central Malay script (http://www.omniglot.com/writing/redjang.htm
) with its angular, rectilinear appearance due to incision on bamboo, but when it began to be written with ink on bark paper (deluwang), it quickly took on cursive shapes that changed away from the earlier shapes, quite drastically in the case of some letters. The same thing happened when the Makassarese in southwest Sulawesi adopted a script nearly identical to Rejang-Central Malay script to write their language instead of the older Lontara script shared with the Bugis (http://www.omniglot.com/writing/lontara.htm
): writing the letters on lontar strips, they made them more curvilinear and changed the stroke order to start from the bottom left and form most of the letter in a single stroke sequence, changing them just enough so that the close relationship wasn't discovered until recently.