Issues with old cloth wire
Circuits utilizing old wire types, often do not include a ground. Outlets on such circuits should not be replaced with 3 prong grounded types unless a proper ground can be added.
Disintegrating Insulation
Used in homes in the home in the first half of the 20th century, cloth wire becomes dangerous as it ages and becomes brittle leaving bare wire exposed. The rubber/cloth insulation around the wire can also melt or catch fire if the wire dissipates too much heat as may happen when too much current is drawn through it.
Moisture from humid air or water from leaks can destroy the cloth. Heat from attics or sun will eventually make the rubber brittle. Left undisturbed, this wire maintains some integrity. The ends of the wires, however, are often found to be quite fragile where switches, outlets and lights are connected. These wires are often manipulated in order make the connections and the insulation is quite friable.
It is not uncommon to find exposed leads inside switch boxes creating shock and arc hazards. Even scarier is finding such wires exposed next to dry lath ready to become tinder should sparks start. More often than not, I will find this situation when going to change light fixtures in lath and plaster ceilings. If there is a drop ceiling, it is not uncommon to find newer wire spliced on to these leads without a junction box.
When feasible, the best solution is to replace the entire run of wire with new. If not feasible, applying properly sized shrink wrap tubing to bare leads is a viable alternative. In all cases, proper boxes should be installed wherever wires terminate or join other wires or fixtures.
Discolored leads
When working with old wires, it is almost always impossible to determine which is neutral and which is hot by color. Color coding of wires only started in 1928, but even those that may have been colored are now so discolored or dirty as to make it almost impossible to determine any longer. When working with such wires, it is always best to use a tester with a known ground or neutral to identify which is hot and which is neutral. Then mark these with properly colored tape. Never assume which is which by how a fixture was wired as that fixture may have been miswired. at some point in the past.
Lack of ground
Homes wired in the first half of the 20th century did not ground receptacles. In fact, the National Electrical Code did not require residential outlets to be grounded until 1974. There are ways to correct this, but not easily achieved in most cases.